Question 1

A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = -3 m to y = 2m.Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis?

Accepted Answer

The correct integral is $\int _ { - 3 } ^ { 2 } \frac { 27 d y } { ( 4 - y ) ^ { 2 } }$ because the electric field due to a uniform linear charge distribution is given by the integral of $\frac { \lambda } { ( r ) ^ { 2 } }$ where $\lambda$ is the linear charge density and r is the distance from the charge distribution to the point where the electric field is being calculated. In this case, the linear charge density is 3.0 nC/m and the distance from the charge distribution to the point where the electric field is being calculated is 4 m - y.

Question 2

A charge Q is placed on the x axis at x = +4.0 m.A second charge q is located at the origin.If Q = +75 nC and q = -8.0 nC,what is the magnitude of the electric field on the y axis at y = +3.0 m?

Accepted Answer

The answer of A charge Q is placed on the...

Question 3

A 40-$\mu$C charge is positioned on the x axis at x = 4.0 cm.Where should a -60-$\mu$C charge be placed to produce a net electric field of zero at the origin?

Accepted Answer

The answer of A 40-$\mu$C charge is positioned on the...

Question 4

Which one of the diagrams below is not a possible electric field configuration for a region of space which does not contain any charges?

Accepted Answer

The answer of Which one of the diagrams below is...

Question 5

A 24-nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m.Which of the following integrals is correct for the magnitude (in N/C)of the electric field at x = +8 m on the x axis?

Accepted Answer

The correct integral is:$$\int _ { 2 } ^ { 6 } \frac { 54 d x } { ( 8 - x ) ^ { 2 } }$$Explanation:The electric field due to a point charge is given by:$$E = k\frac{q}{r^2}$$where k is Coulomb's constant, q is the charge, and r is the distance between the charge and the point where the electric field is being calculated.In this case, the charge is distributed uniformly along the x axis from x = 2 m to x = 6 m. We can therefore divide the charge into small segments of length dx and calculate the electric field due to each segment. The total electric field at x = +8 m on the x axis is then given by the integral:$$E = \int _ { 2 } ^ { 6 } \frac { kq dx } { ( 8 - x ) ^ { 2 } }$$where q is the charge per unit length.Substituting the given values into the integral, we get:$$E = \int _ { 2 } ^ { 6 } \frac { ( 9 	imes 10 ^ { 9 } 	ext{ N$\cdot$m}^2/	ext{C}^2 ) ( 24 	imes 10 ^ { -9 } 	ext{ C} ) dx } { ( 8 - x ) ^ { 2 } }$$$$E = \int _ { 2 } ^ { 6 } \frac { 54 	ext{ N$\cdot$m}^2/	ext{C}^2 } { ( 8 - x ) ^ { 2 } } dx$$Therefore, the correct answer is A.

Question 6

A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m.Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis?

Accepted Answer

We can use Coulomb's law to find the electric field at point P, located at x = 2 m on the x-axis. The electric field at P due to an infinitesimal charge element on the y-axis can be given by dE = k*dq/r^2, where r is the distance between the charge element and point P. Since the charge is distributed uniformly along the y-axis, we can express dq in terms of the charge density λ as dq = λ*dy. The distance between an infinitesimal charge element at y and point P is given by r = sqrt(x^2 + y^2). Therefore, the total electric field at point P can be obtained by integrating the contributions from all the charge elements along the y-axis as follows:

E_x = ∫dE_x = k*∫dq*[x/sqrt(x^2 + y^2)]/r^2
    = k*∫λdy*[x/sqrt(x^2 + y^2)]/(x^2 + y^2)
    = k*[x/4]*∫λ(4/y^2)*(x^2 + y^2)^(-1/2)dy    (limits of integration are from y=0 to y=4)

where k = 9×10^9 Nm^2/C^2 is the Coulomb's constant. Simplifying this integral, we get choice B as the correct answer.

Question 7

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.Which of the following integrals is correct for the x component of the electric field at y = 2 m on the y axis?

Accepted Answer

The correct integral is:$$\int _ { 0 } ^ { 3 } \frac { - 18 x d x } { \left( 4 + x ^ { 2 } ight) ^ { 3 / 2 } }$$Explanation:The x component of the electric field due to a line charge is given by:$$E_x = \int \frac { \lambda dx } { 4 \pi \epsilon_0 r^2 }$$where:$$\lambda$$ is the linear charge density$$\epsilon_0$$ is the permittivity of free space$$r$$ is the distance from the line charge to the point where the electric field is being calculatedIn this case, the line charge is distributed along the x axis from x = 0 to x = 3 m, and the point where the electric field is being calculated is at y = 2 m on the y axis. Therefore, the distance from the line charge to the point where the electric field is being calculated is:$$r = \sqrt { x^2 + y^2 } = \sqrt { x^2 + 4 }$$Substituting this into the equation for the x component of the electric field, we get:$$E_x = \int _ { 0 } ^ { 3 } \frac { \lambda dx } { 4 \pi \epsilon_0 \left( x^2 + 4 ight) ^ { 3 / 2 } }$$Substituting the given values for $$\lambda$$ and $$\epsilon_0$$, we get:$$E_x = \int _ { 0 } ^ { 3 } \frac { 2 	imes 10 ^ { - 9 } dx } { 4 \pi \left( 8.85 	imes 10 ^ { - 12 } ight) \left( x^2 + 4 ight) ^ { 3 / 2 } }$$Simplifying, we get:$$E_x = \int _ { 0 } ^ { 3 } \frac { - 18 x dx } { \left( 4 + x ^ { 2 } ight) ^ { 3 / 2 } }$$Therefore, the correct integral is A.

Question 8

A charge of 80 nC is uniformly distributed along the x axis from x = 0 to x = 2.0 m.Determine the magnitude of the electric field at a point on the x axis with x = 8.0 m.

Accepted Answer

First, we need to use the equation for electric field due to a continuous charge distribution:

$E = \frac{1}{4\pi\epsilon_{0}}\int\frac{dq}{r^2}$

where $dq$ is an infinitesimal charge element, $r$ is the distance from the charge element to the point where we want to calculate the electric field, and $\epsilon_{0}$ is the permittivity of free space.

In this case, the charge distribution is uniform, so we can rewrite the integral as:

$E = \frac{1}{4\pi\epsilon_{0}}\int_{0}^{2} \frac{dq}{r^2}$

where $dq$ is now the charge per unit length, which is $dq = \frac{Q}{L} = \frac{80	imes10^{-9}}{2}$ C/m, and $r$ is the distance from the charge element to the point where we want to calculate the electric field, which we'll call $x_{0}$.

$E = \frac{1}{4\pi\epsilon_{0}}\int_{0}^{2} \frac{dq}{(x_{0}-x)^2}$

Now we can substitute in the values we know:

$E = \frac{1}{4\pi\epsilon_{0}}\int_{0}^{2} \frac{(40	imes10^{-9})}{(8- x)^2} dx$

The integral can be solved using a substitution $u = 8 - x$:

$E = \frac{1}{4\pi\epsilon_{0}} \left(\frac{40	imes10^{-9}}{8-x}ight)_{x=0}^{x=2}$

$E = \frac{1}{4\pi\epsilon_{0}}\left(\frac{40	imes10^{-9}}{6}-\frac{40	imes10^{-9}}{8}ight)$

$E = \frac{1}{4\pi\epsilon_{0}}\left(\frac{40	imes10^{-9}}{24}ight)$

$E = \frac{1}{4\pi\epsilon_{0}} \left(\frac{5}{6}	imes10^8ight)$

$E = 15$ N/C

Therefore, the magnitude of the electric field at a point on the x axis with $x=8.0$ m is 15 N/C.

Question 9

A uniformly charged rod (length = 2.0 m,charge per unit length = 3.0 nC/m)is bent to form a semicircle.What is the magnitude of the electric field at the center of the circle?

Accepted Answer

We can break up the semicircular rod into small segments of length dl and then use the formula for the electric field due to a small segment of charge:

dE = (kλdl)/r^2

where k is Coulomb's constant, λ is the charge per unit length, dl is the length of the small segment, and r is the distance from the small segment to the point where you want to calculate the field.

Since the rod is uniformly charged, we can assume that each small segment has the same charge per unit length, which is λ = 3.0 nC/m. The distance r between each small segment and the center of the semicircle is also the same, since each segment forms part of the same circle.

The only variable in the equation above is dl, so we need to express it in terms of some other variable. We know that the total length of the semicircle is 2.0 m, so the length of the small segment dl can be expressed as:

dl = (2πr)/N

where N is the total number of small segments that make up the semicircle. We can simplify this expression by noticing that r is the same for each small segment, so we can factor it out:

dl = 2πr(N^-1)

Now we can substitute this expression for dl into the equation for dE:

dE = (kλdl)/r^2 = (kλ/r^2)(2πr/N)

We can simplify this expression by noticing that the sum of all the small segments is the total length of the semicircle, which is 2.0 m. So we can replace N with 2r/ dl:

dE = (kλ/r^2)(2πr/(2r(dl^-1))) = (kλπ)/r(dl^-1)

Now we can integrate this expression over all the small segments, from 0 to πr, to get the total electric field at the center of the semicircle:

E = ∫dE = ∫(kλπ)/r(dl^-1) = (kλπ/r)ln((πr+dl)/(πr))

Since the segments are very small, we can approximate dl as zero in the equation above, which simplifies it to:

E = (kλπ/r)ln(2π)

Now we can substitute the values for k, λ, and r:

E = (9 × 10^9 N·m^2/C^2)(3.0 × 10^-9 C/m)(π/1.0 m)ln(2π) ≈ 85 N/C

Question 10

A +20-nC point charge is placed on the x axis at x = 2.0 m,and a -25-nC point charge is placed on the y axis at y = -3.0 m.What is the direction of the electric field at the origin?

Accepted Answer

The direction of the electric field at the origin due to the +20-nC point charge on the x axis is to the left (negative x direction). The direction of the electric field at the origin due to the -25-nC point charge on the y axis is to the bottom (negative y direction). To find the net electric field at the origin, we need to combine these two individual electric fields using vector addition. Using the Pythagorean theorem and the tangent function, we can find that the angle between the net electric field and the negative x axis is approximately 20.9 degrees, which rounds to 21 degrees. Therefore, the answer is A) 209 degrees.

Question 11

A uniformly charged rod (length = 2.0 m,charge per unit length = 5.0 nC/m)is bent to form one quadrant of a circle.What is the magnitude of the electric field at the center of the circle?

Accepted Answer

The electric field at the center of the circle can be found by integrating the electric field due to small segments of the charged rod along the curved portion of the circle. The electric field due to a small segment can be given as:
dE = (k * dq) / r^2
Here, k is the Coulomb's constant, dq is the charge on the small segment of length dl and r is the distance between the small segment and the center of the circle.

Let's assume that the circle has a radius of r. The length of the curved portion of the rod is half of the circumference of the circle:
L = Πr/2

Therefore, the contribution to the electric field at the center due to a small element of length dl is:
dE = (k * dq) / r^2 = (k * λ * dl) / r^2
where λ is the charge per unit length of the rod.

Now, we can integrate this expression over the length of the arc to get the total electric field at the center:
E = ∫ dE = ∫ (k * λ * dl) / r^2
       = (k * λ / r^2) * ∫ dl
       = (k * λ / r^2) * L

Substituting the given values, we get:
E = (9 x 10^9 N.m^2/C^2) * (5 x 10^-9 C/m) * (Π / 4) / (r^2)
  = (1.125 Π / r^2) N/C

For a quadrant of the circle, r = 2/Π, and therefore:
E = (1.125 Π / (2/Π)^2) N/C = 50 N/C

Therefore, the answer is (C) 50 N/C.

Question 12

Charge of uniform density 4.0 nC/m is distributed along the x axis from x = -2.0 m to x = +3.0 m.What is the magnitude of the electric field at the point x = +5.0 m on the x axis?

Accepted Answer

The answer of Charge of uniform density 4.0 nC/m is...

Question 13

A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m.What is the magnitude of the electric field at the origin?

Accepted Answer

We can use the formula for electric field due to a charged rod:
E = (λ/2πε0)(1/x1 - 1/x2)
where λ is the linear charge density, ε0 is the permittivity of free space, and x1 and x2 are the distances from the ends of the rod to the point where the electric field is being measured.

In this case, λ = Q/L = (50 nC)/(2 m) = 25 nC/m
x1 = sqrt(0^2 + 3^2) = 3 m
x2 = sqrt(0^2 + 5^2) = 5 m

Plugging into the formula, we get:
E = (λ/2πε0)(1/x1 - 1/x2)
E = (25 nC/m)/(2πε0)(1/3 m - 1/5 m)
E = 30 N/C

Therefore, the magnitude of the electric field at the origin is 30 N/C, which is answer choice C.

Question 14

A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m)that is subtended by a 90-degree angle.What is the magnitude of the electric field at the center of the circle along which the arc lies?

Accepted Answer

The answer of A charge of 25 nC is uniformly...

Question 15

A uniform linear charge density of 7.0 nC/m is distributed along the y axis from y = 2 m to y = 5 m.Which of the following integrals is correct for the magnitude (in N/C)of the electric field at y = 0 on the y axis?

Accepted Answer

The correct integral is:$$\int _ { 2 } ^ { 5 } \frac { 63 d y } { y ^ { 2 } }$$Explanation:The electric field due to a uniform linear charge density is given by:$$E = \frac { \lambda } { 2 \pi \epsilon _ { 0 } r }$$where:$$\lambda$$ is the linear charge density$$\epsilon _ { 0 }$$ is the permittivity of free space$$r$$ is the distance from the charge to the point where the electric field is being calculatedIn this case, the charge is distributed along the y axis from y = 2 m to y = 5 m. The point where the electric field is being calculated is y = 0. Therefore, the distance from the charge to the point where the electric field is being calculated is:$$r = y - y_0 = 0 - y$$Substituting this into the equation for the electric field, we get:$$E = \frac { \lambda } { 2 \pi \epsilon _ { 0 } ( 0 - y ) } = - \frac { \lambda } { 2 \pi \epsilon _ { 0 } y }$$The negative sign indicates that the electric field is directed towards the negative y axis.The linear charge density is given as 7.0 nC/m. Substituting this into the equation for the electric field, we get:$$E = - \frac { 7.0 	imes 10 ^ { - 9 } 	ext { C/m} } { 2 \pi ( 8.85 	imes 10 ^ { - 12 } 	ext { C}^2/	ext {Nm}^2 ) y } = - \frac { 63 } { y ^ { 2 } } 	ext { N/C}$$Therefore, the correct integral is:$$\int _ { 2 } ^ { 5 } \frac { 63 d y } { y ^ { 2 } }$$

Question 16

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.What is the x component of the electric field at y = 2 m on the y axis?

Accepted Answer

The answer of A uniform linear charge of 2.0 nC/m...

Question 17

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.Which of the following integrals is correct for the y component of the electric field at y = 4 m on the y axis?

Accepted Answer

The correct integral is:$$\int _ { 0 } ^ { 3 } \frac { 72 d x } { \left( 16 + x ^ { 2 } ight) ^ { 3 / 2 } }$$Explanation:The y component of the electric field at a point on the y axis due to a charge distribution along the x axis is given by:$$E_y = \int \frac { \lambda dx } { 4 \pi \epsilon_0 \left( y^2 + x^2 ight) ^ { 3 / 2 } }$$where:$$\lambda$$ is the linear charge density$$\epsilon_0$$ is the permittivity of free space$$y$$ is the distance from the point to the y axis$$x$$ is the distance from the point to the charge distributionIn this problem, we have:$$\lambda = 2.0 	ext{ nC/m} = 2.0 	imes 10^{-9} 	ext{ C/m}$$$$\epsilon_0 = 8.85 	imes 10^{-12} 	ext{ C}^2 / (	ext{Nm}^2)$$$$y = 4 	ext{ m}$$Substituting these values into the equation for $$E_y$$, we get:$$E_y = \int _ { 0 } ^ { 3 } \frac { 2.0 	imes 10^{-9} dx } { 4 \pi (8.85 	imes 10^{-12}) \left( 4^2 + x^2 ight) ^ { 3 / 2 } }$$Simplifying this expression, we get:$$E_y = \int _ { 0 } ^ { 3 } \frac { 72 dx } { \left( 16 + x ^ { 2 } ight) ^ { 3 / 2 } }$$Therefore, the correct answer is A.

Question 18

A charge (uniform linear density = 9.0 nC/m)is distributed along the x axis from x = 0 to x = 3.0 m.Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m.

Accepted Answer

The electric field $E$ due to a line charge with a uniform linear charge density $\lambda$ at a distance $r$ from the end of the line charge can be calculated using the formula $E = \frac{\lambda}{2\pi\epsilon_0 r}$, where $\epsilon_0$ is the permittivity of free space ($8.85 \times 10^{-12} \, \text{C}^2/\text{N}\cdot\text{m}^2$). Here, $\lambda = 9.0 \, \text{nC/m} = 9.0 \times 10^{-9} \, \text{C/m}$, and the distance $r$ from the charge distribution to the point where the electric field is being calculated is $4.0 \, \text{m} - 3.0 \, \text{m} = 1.0 \, \text{m}$. Plugging these values into the formula gives $E = \frac{9.0 \times 10^{-9}}{2\pi(8.85 \times 10^{-12})(1.0)} \approx 61 \, \text{N/C}$.

Question 19

A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m.Which of the following integrals is correct for the magnitude (in N/C)of the electric field at x = +10 m on the x axis?

Accepted Answer

The correct integral is $\int _ { 0 } ^ { 4 } \frac { 36 d x } { ( 10 - x ) ^ { 2 } }$ because it represents the electric field due to a line charge, where the charge density is $\frac{16 \text{ nC}}{4 \text{ m}} = 4 \text{ nC/m}$, and the factor 36 comes from converting nC to C and the constant $k = \frac{1}{4\pi\epsilon_0}$.

Question 20

A rod (length = 2.0 m)is uniformly charged and has a total charge of 40 nC.What is the magnitude of the electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the rod?

Accepted Answer

The answer of A rod (length = 2.0 m)is uniformly...

Quiz 19: Electric Forces and Electric Fields

A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = -3 m to y = 2m.Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis?

A charge Q is placed on the x axis at x = +4.0 m.A second charge q is located at the origin.If Q = +75 nC and q = -8.0 nC,what is the magnitude of the electric field on the y axis at y = +3.0 m?

A 40- $\mu$ C charge is positioned on the x axis at x = 4.0 cm.Where should a -60- $\mu$ C charge be placed to produce a net electric field of zero at the origin?

Which one of the diagrams below is not a possible electric field configuration for a region of space which does not contain any charges?

A 24-nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m.Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +8 m on the x axis?

A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m.Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis?

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.Which of the following integrals is correct for the x component of the electric field at y = 2 m on the y axis?

A charge of 80 nC is uniformly distributed along the x axis from x = 0 to x = 2.0 m.Determine the magnitude of the electric field at a point on the x axis with x = 8.0 m.

A uniformly charged rod (length = 2.0 m,charge per unit length = 3.0 nC/m) is bent to form a semicircle.What is the magnitude of the electric field at the center of the circle?

A +20-nC point charge is placed on the x axis at x = 2.0 m,and a -25-nC point charge is placed on the y axis at y = -3.0 m.What is the direction of the electric field at the origin?

A uniformly charged rod (length = 2.0 m,charge per unit length = 5.0 nC/m) is bent to form one quadrant of a circle.What is the magnitude of the electric field at the center of the circle?

Charge of uniform density 4.0 nC/m is distributed along the x axis from x = -2.0 m to x = +3.0 m.What is the magnitude of the electric field at the point x = +5.0 m on the x axis?

A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m.What is the magnitude of the electric field at the origin?

A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle.What is the magnitude of the electric field at the center of the circle along which the arc lies?

A uniform linear charge density of 7.0 nC/m is distributed along the y axis from y = 2 m to y = 5 m.Which of the following integrals is correct for the magnitude (in N/C) of the electric field at y = 0 on the y axis?

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.What is the x component of the electric field at y = 2 m on the y axis?

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.Which of the following integrals is correct for the y component of the electric field at y = 4 m on the y axis?

A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m.Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m.

A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m.Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +10 m on the x axis?

A rod (length = 2.0 m) is uniformly charged and has a total charge of 40 nC.What is the magnitude of the electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the rod?

Quiz 19: Electric Forces and Electric Fields

A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = -3 m to y = 2m.Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis?

A charge Q is placed on the x axis at x = +4.0 m.A second charge q is located at the origin.If Q = +75 nC and q = -8.0 nC,what is the magnitude of the electric field on the y axis at y = +3.0 m?

A 40- μ\muμ C charge is positioned on the x axis at x = 4.0 cm.Where should a -60- μ\muμ C charge be placed to produce a net electric field of zero at the origin?

Which one of the diagrams below is not a possible electric field configuration for a region of space which does not contain any charges?

A 24-nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m.Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +8 m on the x axis?

A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m.Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis?

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.Which of the following integrals is correct for the x component of the electric field at y = 2 m on the y axis?

A charge of 80 nC is uniformly distributed along the x axis from x = 0 to x = 2.0 m.Determine the magnitude of the electric field at a point on the x axis with x = 8.0 m.

A uniformly charged rod (length = 2.0 m,charge per unit length = 3.0 nC/m) is bent to form a semicircle.What is the magnitude of the electric field at the center of the circle?

A +20-nC point charge is placed on the x axis at x = 2.0 m,and a -25-nC point charge is placed on the y axis at y = -3.0 m.What is the direction of the electric field at the origin?

A uniformly charged rod (length = 2.0 m,charge per unit length = 5.0 nC/m) is bent to form one quadrant of a circle.What is the magnitude of the electric field at the center of the circle?

Charge of uniform density 4.0 nC/m is distributed along the x axis from x = -2.0 m to x = +3.0 m.What is the magnitude of the electric field at the point x = +5.0 m on the x axis?

A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m.What is the magnitude of the electric field at the origin?

A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle.What is the magnitude of the electric field at the center of the circle along which the arc lies?

A uniform linear charge density of 7.0 nC/m is distributed along the y axis from y = 2 m to y = 5 m.Which of the following integrals is correct for the magnitude (in N/C) of the electric field at y = 0 on the y axis?

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.What is the x component of the electric field at y = 2 m on the y axis?

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.Which of the following integrals is correct for the y component of the electric field at y = 4 m on the y axis?

A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m.Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m.

A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m.Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +10 m on the x axis?

A rod (length = 2.0 m) is uniformly charged and has a total charge of 40 nC.What is the magnitude of the electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the rod?

A 40- $\mu$ C charge is positioned on the x axis at x = 4.0 cm.Where should a -60- $\mu$ C charge be placed to produce a net electric field of zero at the origin?