Question 1

If a doubly-ionized oxygen atom (O^-2)is accelerated from rest by going through a potential difference of 32 V,what will be the change in its kinetic energy?

Accepted Answer

The change in kinetic energy of a charged particle is equal to the charge of the particle multiplied by the potential difference. A doubly-ionized oxygen atom has a charge of -2e, so the change in kinetic energy is 2e * 32 V = 64 eV.

Question 2

An electron in a TV picture tube is accelerated through a potential difference of 10 kV before it hits the screen.What is the kinetic energy of the electron in electron volts? (1 eV = 1.6 × 10−¹⁹ J)

Accepted Answer

The kinetic energy of the electron can be found using the formula: 
KE = qV
where KE is the kinetic energy, q is the charge of the electron, and V is the potential difference.
The charge of the electron is -1.6 x 10^-19 C and the potential difference is 10,000 V.
Therefore,
KE = -1.6 x 10^-19 C x 10,000 V
KE = -1.6 x 10^-15 J
Converting from joules to electron volts:
KE = (-1.6 x 10^-15 J) / (1.6 x 10^-19 J/eV)
KE = -1.0 x 10^4 eV
Since the kinetic energy cannot be negative (we would interpret it as zero in this context), the magnitude of the answer is 1.0E+4 eV, which is the correct choice.

Question 3

Two particles,each of charge 2.5 × 10^-19 C,are 4.8 × 10^-5 m apart.What is the change in potential energy if they are brought 2.4 × 10^-5 m closer together? (k_e = 8.99 × 10⁹ N·m²/C²)

Accepted Answer

The potential energy between two charges is given by U=k(q1q2)/r, where k is Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them.
So, the initial potential energy is U=k(q1q2)/r1, where r1=4.8×10^-5 m.
The final potential energy is U=k(q1q2)/r2, where r2=2.4×10^-5 m.
Subtracting these two, we get the change in potential energy:
ΔU=Uf-Ui=k(q1q2)(1/r2-1/r1)=8.99×10^9(2.5×10^-19)^2(1/2.4×10^-5-1/4.8×10^-5)=1.2×10^-23 J.

Therefore, the answer is (A) 1.2E-23 J.

Question 4

When charge Q₁ is placed at point P₁,the resulting potential at point P is V₁.When Q₂ is placed at point P₂ after Q₁ is in position at P₁,the resulting potential at P becomes V₂.What is the potential at point P if charge Q₁ is then removed?

Accepted Answer

The potential at a point due to multiple charges is the algebraic sum of the potentials due to each charge individually. When Q₁ is removed, the potential at point P is solely due to Q₂, which is already included in the total potential V₂. Therefore, the potential due to Q₁ must be subtracted from V₂ to find the new potential at P.

Question 5

Electrons in an x-ray machine are accelerated from rest through a potential difference of 60 000 V.What is the kinetic energy of each of these electrons in eV?

Accepted Answer

The kinetic energy gained by an electron accelerated through a potential difference V is given by:

K = qV

where q is the charge of the electron and V is the potential difference.

For an electron, q = -1.6 x 10^-19 C.

Substituting this value and the given potential difference of 60 000 V, we get:

K = (-1.6 x 10^-19 C) x (60 000 V) = -9.6 x 10^-15 J

This value can be converted to electron volts (eV) using the conversion factor 1 eV = 1.6 x 10^-19 J:

K = (-9.6 x 10^-15 J) / (1.6 x 10^-19 J/eV) = -60 keV

Note that the negative sign indicates that the electron has lost potential energy and gained kinetic energy. To obtain the absolute value of the kinetic energy, we ignore the negative sign:

|K| = 60 keV

Therefore, the kinetic energy of each electron in the x-ray machine is 60 keV. The answer choice that corresponds to this is D.

Question 6

Find the electrical potential at 0.25 m from a point charge of 7.0 μC.(k_e = 8.99 × 10⁹ N⋅m²/C²)

Accepted Answer

The electrical potential V at a distance r from a point charge Q is given by V = k_e * Q / r. Substituting the given values: V = (8.99 × 10^9 N⋅m²/C²) * (7.0 × 10^-6 C) / 0.25 m = 2.5 × 10^5 V.

Question 7

When charges q_a,q_b,and q_c are placed respectively at the corners a,b,and c of a right triangle,the potential at the midpoint of the hypotenuse is 24 V.When the charge q_a is removed,the potential at the midpoint becomes 17 V.When,instead,the charge q_b is removed (q_a and q_c both in place),the potential at the midpoint becomes 13 V.What is the potential at the midpoint if both charges q_a and q_c are removed?

Accepted Answer

The potential at the midpoint with all charges is 24 V. Removing q_a drops the potential to 17 V, indicating q_a contributes 7 V. Removing q_b instead drops it to 13 V, indicating q_b contributes 11 V. Thus, removing both q_a and q_c (given q_a's 7 V contribution), and knowing q_b alone gives 13 V, the potential with only q_b is 13 V, matching option A.

Question 8

Consider two charged spheres,one with charge +2 C and the other with −2 C.A proton (a positively charged particle)is at the point halfway between the spheres.What is not zero?

Accepted Answer

The force on the proton is not zero because it would experience a net force due to the two charged spheres. The potential energy of the proton is also not zero because there is an interaction between the proton and the two charged spheres. However, the work to move the proton from infinity to that point is zero because the electric field is zero at infinity and the proton would not require any work to be moved to the halfway point between the spheres where the electric field is non-zero.

Question 9

Two point charges of values +3.6 and +6.9 μC are separated by 0.40 m.What is the electrical potential at the point midway between the two point charges? (k_e = 8.99 × 10⁹ N⋅m²/C²)

Accepted Answer

The answer of Two point charges of values +3.6 and...

Question 10

A point charge of +2.5 μC is located at the origin of a coordinate system and a second point charge of −5.6 μC is at x = 1.9 m.At what point on the x axis is the electrical potential zero?

Accepted Answer

The electric potential along the x-axis due to the point charge at the origin is given by V1 = kQ1/x. The electric potential due to the second charge at x = 1.9 m is given by V2 = kQ2/(x-1.9). The total electric potential V(x) along the x-axis is the sum of these two potentials. Setting V(x) = 0 and solving for x gives x = 0.59 m. Therefore, the answer is C.

Question 11

Which of the following characteristics are held in common by both gravitational and electrostatic forces when dealing with either point masses or charges?

Accepted Answer

All of the above choices are valid for both gravitational and electrostatic forces when dealing with point masses or charges. The inverse square distance law applies to both forces, the forces are conservative, and the potential energy is a function of distance of separation.

Question 12

A solid metal sphere of radius r is inside a metal concentric spherical shell of inner radius 2r and outer radius 3r.A charge is place on the solid metal sphere and it is found that the potential at its surface is V₁ (at r)and that the potential at the outer surface of the spherical shell is V₃ (at 3r).In terms of V₁ and V₃,what is the potential at the inner surface of the metal shell (at 2r)?

Accepted Answer

The answer of A solid metal sphere of radius r...

Question 13

If the plane x = 4 m is an equipotential surface,in which of the following directions can the electric field be in the region immediately adjacent to this plane?

Accepted Answer

An equipotential surface is a surface in which every point has the same electric potential. Therefore, the electric field must be perpendicular to the equipotential surface. Since the equipotential surface is given by x = 4 m, the electric field must be in the direction of the gradient of x, which is the positive x direction. Therefore, the correct answer is C) the positive x direction.

Question 14

At what distance from a point charge of 8.0 μC would the electrical potential be 4.8 × 10⁴ V? (k_e = 8.99 × 10⁹ N⋅m²/C²)

Accepted Answer

The answer of At what distance from a point charge...

Question 15

If the distance between two negative point charges is increased by a factor of three,the resultant potential energy is what factor times the initial potential energy?

Accepted Answer

The potential energy between two point charges is inversely proportional to the distance between them. If the distance is increased by a factor of three, the potential energy becomes 1/3 of the initial value.

Question 16

A point charge of +4.0 μC is located at the origin of a coordinate system and a second point charge of −6.6 μC is at x = 1.7 m.What is the electric potential at the x = 0.85 m point? (k_e = 8.99 × 10⁹ N⋅m²/C²)

Accepted Answer

The electric potential at a point due to a point charge can be calculated using the equation:

V = kQ/r

where k is the Coulomb's constant (8.99 × 10^9 N·m^2/C^2), Q is the charge of the point charge, and r is the distance between the point charge and the point where electric potential is being measured.

Using this equation, we can calculate the electric potential at x=0.85 m as:

V = (8.99 × 10^9 N·m^2/C^2) * [(4.0 μC)/0.85 m - (6.6 μC)/1.85 m]
V = - 2.7 × 10^4 V = -2.7 × 10^14 V

Therefore, the best choice is D, with the calculated electric potential of -2.7 × 10^14 V at x=0.85 m.

Question 17

There is a hollow,conducting,uncharged sphere with a negative charge inside the sphere.Consider the electrical potential at the inner and outer surfaces of the sphere.Which of the following is true?

Accepted Answer

Since the sphere is conductive, the charges inside it will always spread out evenly on the surface. Therefore, the potential on both the inner and outer surfaces will be equal. However, since there is a negative charge inside the sphere, the potential will be negative. Hence, the potentials on both surfaces are equal but not zero. Therefore, the correct choice is D.

Question 18

Two point charges of values +2.0 and +5.5 μC,respectively,are separated by 0.50 m.What is the potential energy of this 2-charge system? (k_e = 8.99 × 10⁹ N⋅m²/C²)

Accepted Answer

The answer of Two point charges of values +2.0 and...

Question 19

When charges q_a,q_b,and q_c are placed respectively at the corners a,b,and c of a right triangle,the potential at the midpoint of the hypotenuse is 20 V.When the charge q_a is removed,the potential at the midpoint becomes 15 V.When,instead,the charge q_b is removed (q_a and q_c both in place),the potential at the midpoint becomes 12 V.What is the potential at the midpoint if only the charge q_c is removed from the array of charges?

Accepted Answer

The potential at the midpoint with all charges is 20 V. Removing q_a drops it to 15 V, indicating q_a contributes 5 V. Removing q_b drops it to 12 V, indicating q_b contributes 8 V. Thus, q_c must contribute 7 V (20 V - 5 V - 8 V). Removing q_c, the potential is 20 V - 7 V = 13 V.

Question 20

A solid conducting sphere of 10-cm radius has a net charge of 18 nC.If the potential at infinity is taken as zero,what is the potential at the center of the sphere?

Accepted Answer

The potential at the center of a solid conducting sphere is given by $V = \frac{kQ}{r}$, where $k$ is Coulomb's constant ($9 \times 10^9 \, \text{Nm}^2/\text{C}^2$), $Q$ is the net charge on the sphere, and $r$ is the radius of the sphere. Substituting the given values ($Q = 18 \, \text{nC} = 18 \times 10^{-9} \, \text{C}$ and $r = 10 \, \text{cm} = 0.1 \, \text{m}$), we find $V = \frac{9 \times 10^9 \times 18 \times 10^{-9}}{0.1} = 1.62 \times 10^9 \, \text{V}$, which matches the format of choice C.

Quiz 16: Electrical Energy and Capacitance

If a doubly-ionized oxygen atom (O^-2) is accelerated from rest by going through a potential difference of 32 V,what will be the change in its kinetic energy?

An electron in a TV picture tube is accelerated through a potential difference of 10 kV before it hits the screen.What is the kinetic energy of the electron in electron volts? (1 eV = 1.6 × 10−¹⁹ J)

Two particles,each of charge 2.5 × 10^-19 C,are 4.8 × 10^-5 m apart.What is the change in potential energy if they are brought 2.4 × 10^-5 m closer together? (k_e = 8.99 × 10⁹ N·m²/C²)

When charge Q₁ is placed at point P₁,the resulting potential at point P is V₁.When Q₂ is placed at point P₂ after Q₁ is in position at P₁,the resulting potential at P becomes V₂.What is the potential at point P if charge Q₁ is then removed?

Electrons in an x-ray machine are accelerated from rest through a potential difference of 60 000 V.What is the kinetic energy of each of these electrons in eV?

Find the electrical potential at 0.25 m from a point charge of 7.0 μC.(k_e = 8.99 × 10⁹ N⋅m²/C²)

Consider two charged spheres,one with charge +2 C and the other with −2 C.A proton (a positively charged particle) is at the point halfway between the spheres.What is not zero?

Two point charges of values +3.6 and +6.9 μC are separated by 0.40 m.What is the electrical potential at the point midway between the two point charges? (k_e = 8.99 × 10⁹ N⋅m²/C²)

A point charge of +2.5 μC is located at the origin of a coordinate system and a second point charge of −5.6 μC is at x = 1.9 m.At what point on the x axis is the electrical potential zero?

Which of the following characteristics are held in common by both gravitational and electrostatic forces when dealing with either point masses or charges?

If the plane x = 4 m is an equipotential surface,in which of the following directions can the electric field be in the region immediately adjacent to this plane?

At what distance from a point charge of 8.0 μC would the electrical potential be 4.8 × 10⁴ V? (k_e = 8.99 × 10⁹ N⋅m²/C²)

If the distance between two negative point charges is increased by a factor of three,the resultant potential energy is what factor times the initial potential energy?

A point charge of +4.0 μC is located at the origin of a coordinate system and a second point charge of −6.6 μC is at x = 1.7 m.What is the electric potential at the x = 0.85 m point? (k_e = 8.99 × 10⁹ N⋅m²/C²)

There is a hollow,conducting,uncharged sphere with a negative charge inside the sphere.Consider the electrical potential at the inner and outer surfaces of the sphere.Which of the following is true?

Two point charges of values +2.0 and +5.5 μC,respectively,are separated by 0.50 m.What is the potential energy of this 2-charge system? (k_e = 8.99 × 10⁹ N⋅m²/C²)

A solid conducting sphere of 10-cm radius has a net charge of 18 nC.If the potential at infinity is taken as zero,what is the potential at the center of the sphere?

Quiz 16: Electrical Energy and Capacitance

If a doubly-ionized oxygen atom (O-2) is accelerated from rest by going through a potential difference of 32 V,what will be the change in its kinetic energy?

An electron in a TV picture tube is accelerated through a potential difference of 10 kV before it hits the screen.What is the kinetic energy of the electron in electron volts? (1 eV = 1.6 × 10−19 J)

Two particles,each of charge 2.5 × 10-19 C,are 4.8 × 10-5 m apart.What is the change in potential energy if they are brought 2.4 × 10-5 m closer together? (ke = 8.99 × 109 N·m2/C2)

When charge Q1 is placed at point P1,the resulting potential at point P is V1.When Q2 is placed at point P2 after Q1 is in position at P1,the resulting potential at P becomes V2.What is the potential at point P if charge Q1 is then removed?

Electrons in an x-ray machine are accelerated from rest through a potential difference of 60 000 V.What is the kinetic energy of each of these electrons in eV?

Find the electrical potential at 0.25 m from a point charge of 7.0 μC.(ke = 8.99 × 109 N⋅m2/C2)

Consider two charged spheres,one with charge +2 C and the other with −2 C.A proton (a positively charged particle) is at the point halfway between the spheres.What is not zero?

Two point charges of values +3.6 and +6.9 μC are separated by 0.40 m.What is the electrical potential at the point midway between the two point charges? (ke = 8.99 × 109 N⋅m2/C2)

A point charge of +2.5 μC is located at the origin of a coordinate system and a second point charge of −5.6 μC is at x = 1.9 m.At what point on the x axis is the electrical potential zero?

Which of the following characteristics are held in common by both gravitational and electrostatic forces when dealing with either point masses or charges?

If the plane x = 4 m is an equipotential surface,in which of the following directions can the electric field be in the region immediately adjacent to this plane?

At what distance from a point charge of 8.0 μC would the electrical potential be 4.8 × 104 V? (ke = 8.99 × 109 N⋅m2/C2)

If the distance between two negative point charges is increased by a factor of three,the resultant potential energy is what factor times the initial potential energy?

A point charge of +4.0 μC is located at the origin of a coordinate system and a second point charge of −6.6 μC is at x = 1.7 m.What is the electric potential at the x = 0.85 m point? (ke = 8.99 × 109 N⋅m2/C2)

There is a hollow,conducting,uncharged sphere with a negative charge inside the sphere.Consider the electrical potential at the inner and outer surfaces of the sphere.Which of the following is true?

Two point charges of values +2.0 and +5.5 μC,respectively,are separated by 0.50 m.What is the potential energy of this 2-charge system? (ke = 8.99 × 109 N⋅m2/C2)

A solid conducting sphere of 10-cm radius has a net charge of 18 nC.If the potential at infinity is taken as zero,what is the potential at the center of the sphere?

If a doubly-ionized oxygen atom (O^-2) is accelerated from rest by going through a potential difference of 32 V,what will be the change in its kinetic energy?

An electron in a TV picture tube is accelerated through a potential difference of 10 kV before it hits the screen.What is the kinetic energy of the electron in electron volts? (1 eV = 1.6 × 10−¹⁹ J)

Two particles,each of charge 2.5 × 10^-19 C,are 4.8 × 10^-5 m apart.What is the change in potential energy if they are brought 2.4 × 10^-5 m closer together? (k_e = 8.99 × 10⁹ N·m²/C²)

When charge Q₁ is placed at point P₁,the resulting potential at point P is V₁.When Q₂ is placed at point P₂ after Q₁ is in position at P₁,the resulting potential at P becomes V₂.What is the potential at point P if charge Q₁ is then removed?

Find the electrical potential at 0.25 m from a point charge of 7.0 μC.(k_e = 8.99 × 10⁹ N⋅m²/C²)

Two point charges of values +3.6 and +6.9 μC are separated by 0.40 m.What is the electrical potential at the point midway between the two point charges? (k_e = 8.99 × 10⁹ N⋅m²/C²)

At what distance from a point charge of 8.0 μC would the electrical potential be 4.8 × 10⁴ V? (k_e = 8.99 × 10⁹ N⋅m²/C²)

A point charge of +4.0 μC is located at the origin of a coordinate system and a second point charge of −6.6 μC is at x = 1.7 m.What is the electric potential at the x = 0.85 m point? (k_e = 8.99 × 10⁹ N⋅m²/C²)

Two point charges of values +2.0 and +5.5 μC,respectively,are separated by 0.50 m.What is the potential energy of this 2-charge system? (k_e = 8.99 × 10⁹ N⋅m²/C²)