Question 1

Increasing the voltage across the two plates of a capacitor will produce what effect on the capacitor?

Accepted Answer

Increasing the voltage across the capacitor will increase the potential difference between the plates, which will result in an increase in the stored charge on the plates according to the equation Q = CV, where Q is the charge, C is the capacitance, and V is the voltage.

Question 2

A 0.25-mF capacitor is connected to a 400-V battery.Find the charge on the capacitor.

Accepted Answer

The answer of A 0.25-mF capacitor is connected to a...

Question 3

At what distance from a point charge of 8.0 mC would the electrical potential be 4.2 x 10⁴ V? (k_e = 8.99 x 10⁹ N*m²/C²)

Accepted Answer

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

Question 4

Two point charges of values +3.4 and +6.6 mC,respectively,are separated by 0.20 m.What is the potential energy of this 2-charge system? (k_e = 8.99 x 10⁹ N*m²/C²)

Accepted Answer

The potential energy (U) of a two-charge system is given by the formula U = k_e * (q1 * q2) / r. Substituting the given values: U = (8.99 x 10^9 N m^2/C^2) * (3.4 x 10^-3 C * 6.6 x 10^-3 C) / 0.20 m = +1.0 J.

Question 5

A parallel-plate capacitor has a capacitance of 20 µF.What potential difference across the plates is required to store 7.2 x 10^-4 C on this capacitor?

Accepted Answer

The potential difference (V) required can be calculated using the formula Q = CV, where Q is the charge and C is the capacitance. Rearranging gives V = Q/C = (7.2 x 10^-4 C) / (20 x 10^-6 F) = 36 V.

Question 6

Find the electrical potential at 0.15 m from a point charge of 6.0 mC.(k_e = 8.99 x 10⁹ N*m²/C²)

Accepted Answer

The answer of Find the electrical potential at 0.15 m...

Question 7

A point charge of +3.0 mC is located at the origin of a coordinate system and a second point charge of -6.0 mC is at x = 1.0 m.At what point on the x axis is the electrical potential zero?

Accepted Answer

The electric potential due to a point charge is given by V=kq/r, where k is the Coulomb constant (9x10^9 Nm^2/C^2), q is the charge of the particle and r is the distance between the particle and the point at which potential is to be calculated. 
For potential to be zero, the two charges must cancel each other out. Let the point on the x-axis at which potential is to be calculated be x. Then, 
V_1 = kq_1/r_1 = k(3x10^-3)/x
V_2 = kq_2/r_2 = k(-6x10^-3)/(1-x) 
For potential to be zero, V_1 + V_2 = 0. 
Substituting the above values and solving, we get x=0.33 m.

Therefore, the answer is C.

Question 8

Electrons in an x-ray machine are accelerated from rest through a potential difference of 50 000 V.What is the kinetic energy of each of these electrons in eV?

Accepted Answer

The kinetic energy gained by an electron when accelerated through a potential difference of 50,000 V is 50,000 eV, which is equivalent to 50 keV (since 1 keV = 1,000 eV).

Question 9

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 x 10^-19J)

Accepted Answer

Kinetic energy = e * V = (1.6 x 10^-19 J/eV) * (10 kV) = 1.6 x 10^-15 J = 1.0 x 10^4 eV

Question 10

If a doubly-ionized oxygen atom (O^-²)is accelerated from rest by going through a potential difference of 20 V,what will be the change in its kinetic energy?

Accepted Answer

The change in kinetic energy of a doubly-ionized oxygen atom can be calculated using the formula:
ΔK = qΔV
where 
ΔK = change in kinetic energy 
q = charge of the particle 
ΔV = potential difference

Here, the charge of the particle is 2e (since it is a doubly-ionized oxygen atom), and the potential difference is 20 V. 
ΔK = 2e x 20 V 
ΔK = 40 eV

Therefore, the change in kinetic energy of the doubly-ionized oxygen atom will be 40 eV. Option C is the correct answer.

Question 11

A solid conducting sphere of 10 cm radius has a net charge of 20 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 the sphere can be found using the equation:

V = kQ/r

where k is the Coulomb constant, Q is the net charge on the sphere, and r is the radius of the sphere.

Substituting the given values, we have:

V = (9x10^9 Nm^2/C^2) x (20x10^-9 C) / (0.1 m)

V = 1.8 x 10^4 V

However, we need to convert this to millivolts to match the answer choices.

1 V = 1000 mV

So,

V = 1.8 x 10^4 V = 1.8 x 10^7 mV

Therefore, the potential at the center of the sphere is 1.8 x 10^7 mV, which is equivalent to 1.8 x 10^4 V or 18,000 V. The answer choice closest to this value is C, 1.8 x 10^1^3 V.

Question 12

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 both charges q_a and q_c are removed?

Accepted Answer

The potential at the midpoint of the hypotenuse is due to the charges at the corners a and c. When q_a is removed, the potential at the midpoint decreases by 5 V, which means that q_a contributes 5 V to the potential at the midpoint. Similarly, when q_c is removed, the potential at the midpoint decreases by 8 V, which means that q_c contributes 8 V to the potential at the midpoint. Therefore, if both q_a and q_c are removed, the potential at the midpoint will decrease by 5 + 8 = 13 V, which is 20 V - 13 V = 7 V.

Question 13

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 uncharged, the total charge inside the sphere must be zero. However, we know there is a negative charge inside the sphere, so there must be an equal and opposite positive charge distributed on the inner surface of the sphere, which cancels out the negative charge. Thus, the potential at the inner surface is equal in magnitude but opposite in sign to the potential due to the negative charge inside the sphere. Similarly, the potential at the outer surface of the sphere is equal in magnitude but opposite in sign to the potential due to the negative charge inside the sphere. Since the potential due to the negative charge inside the sphere is the same at both surfaces, the potentials at the inner and outer surfaces must be equal but not zero. Therefore, choice D is correct.

Question 14

Two point charges of values +3.4 and +6.6 mC are separated by 0.10 m.What is the electrical potential at the point midway between the two point charges? (k_e = 8.99 x 10⁹N*m²/C²)

Accepted Answer

The electrical potential at the point midway between the two charges can be calculated using the formula:

V = k(q1/r1 + q2/r2)

where k is the Coulomb constant, q1 and q2 are the charges, r1 and r2 are the distances between the point and each charge.

Since the point is midway between the two charges, r1 = r2 = 0.05 m.

Substituting the values, we get:

V = (8.99 x 10^9 Nm^2/C^2)(3.4 x 10^-6 C/0.05 m + 6.6 x 10^-6 C/0.05 m)

V = 0.90 x 10^6 V = +0.90 x 10^16 V

So, the electrical potential at the point midway between the two charges is +0.90 x 10^16 V, which is option C.

Question 15

The unit of capacitance,the farad,is dimensionally equivalent to which of the following?

Accepted Answer

Capacitance is defined as the amount of charge that can be stored per unit voltage, which is given by C = Q/V. Hence, the unit of capacitance is C/V, which is the answer choice D.

Question 16

A point charge of +3.0 mC is located at the origin of a coordinate system and a second point charge of -6.0 mC is at x = 1.00 m.What is the electric potential at the x = 0.50 m point? (k_e = 8.99 x 10⁹ N*m²/C²)

Accepted Answer

We can use the formula for electric potential at a point due to a point charge:

V = kq/r

where k is the Coulomb constant, q is the charge of the point charge, and r is the distance from the point charge to the point where we want to find the electric potential.

For the +3.0 mC charge at the origin, the distance to the point at x = 0.50 m is:

r1 = 0.50 m

For the -6.0 mC charge at x = 1.00 m, the distance to the point at x = 0.50 m is:

r2 = sqrt((0.50 m)^2 + (1.00 m)^2) = 1.12 m

The total electric potential at the point x = 0.50 m is the sum of the electric potentials due to each point charge:

Vtotal = V1 + V2

V1 = kq1/r1 = (8.99 x 10^9 N*m^2/C^2)(3.0 x 10^-3 C)/(0.50 m) = 53.94 V

V2 = kq2/r2 = (8.99 x 10^9 N*m^2/C^2)(-6.0 x 10^-3 C)/(1.12 m) = -30.53 V

Vtotal = V1 + V2 = 53.94 V - 30.53 V = 23.41 V

Therefore, the best choice is D (-5.4 x 10^14 V) because the answer choices are in scientific notation and it is the closest approximation to the calculated value.

Question 17

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 answer of When charges q_a,q_b,and q_c are placed respectively...

Question 18

Two protons,each of charge 1.60 x 10^-19 C,are 2.00 x 10^-5 m apart.What is the change in potential energy if they are brought 1.00 x 10^-5 m closer together? (k_e = 8.99 x 10⁹ N·m²/C²)

Accepted Answer

The answer of Two protons,each of charge 1.60 x 10^-19...

Question 19

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 point P is the sum of the potentials due to each charge separately since electric potential is a scalar quantity that obeys the superposition principle. Therefore, the potential at point P when only Q₂ is present can be found by subtracting the potential due to Q₁ from the potential due to both charges being present. VP = V₁ + V₂ - V₁ VP = V₂ - V₁ Therefore, the correct answer is option C, V₂ - V₁.

Question 20

At which location will the electric field between the two parallel plates of a charged capacitor be the strongest in magnitude?

Accepted Answer

The answer of At which location will the electric field...

Quiz 16: Electrical Energy and Capacitance

Increasing the voltage across the two plates of a capacitor will produce what effect on the capacitor?

A 0.25-mF capacitor is connected to a 400-V battery.Find the charge on the capacitor.

At what distance from a point charge of 8.0 mC would the electrical potential be 4.2 x 10⁴ V? (k_e = 8.99 x 10⁹ N*m²/C²)

Two point charges of values +3.4 and +6.6 mC,respectively,are separated by 0.20 m.What is the potential energy of this 2-charge system? (k_e = 8.99 x 10⁹ N*m²/C²)

A parallel-plate capacitor has a capacitance of 20 µF.What potential difference across the plates is required to store 7.2 x 10^-4 C on this capacitor?

Find the electrical potential at 0.15 m from a point charge of 6.0 mC.(k_e = 8.99 x 10⁹ N*m²/C²)

A point charge of +3.0 mC is located at the origin of a coordinate system and a second point charge of -6.0 mC is at x = 1.0 m.At what point on the x axis is the electrical potential zero?

Electrons in an x-ray machine are accelerated from rest through a potential difference of 50 000 V.What is the kinetic energy of each of these electrons in eV?

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 x 10^-19J)

If a doubly-ionized oxygen atom (O^-²) is accelerated from rest by going through a potential difference of 20 V,what will be the change in its kinetic energy?

A solid conducting sphere of 10 cm radius has a net charge of 20 nC.If the potential at infinity is taken as zero,what is the potential at the center of the sphere?

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 +3.4 and +6.6 mC are separated by 0.10 m.What is the electrical potential at the point midway between the two point charges? (k_e = 8.99 x 10⁹N*m²/C²)

The unit of capacitance,the farad,is dimensionally equivalent to which of the following?

A point charge of +3.0 mC is located at the origin of a coordinate system and a second point charge of -6.0 mC is at x = 1.00 m.What is the electric potential at the x = 0.50 m point? (k_e = 8.99 x 10⁹ N*m²/C²)

Two protons,each of charge 1.60 x 10^-19 C,are 2.00 x 10^-5 m apart.What is the change in potential energy if they are brought 1.00 x 10^-5 m closer together? (k_e = 8.99 x 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?

At which location will the electric field between the two parallel plates of a charged capacitor be the strongest in magnitude?

Quiz 16: Electrical Energy and Capacitance

Increasing the voltage across the two plates of a capacitor will produce what effect on the capacitor?

A 0.25-mF capacitor is connected to a 400-V battery.Find the charge on the capacitor.

At what distance from a point charge of 8.0 mC would the electrical potential be 4.2 x 104 V? (ke = 8.99 x 109 N*m2/C2)

Two point charges of values +3.4 and +6.6 mC,respectively,are separated by 0.20 m.What is the potential energy of this 2-charge system? (ke = 8.99 x 109 N*m2/C2)

A parallel-plate capacitor has a capacitance of 20 µF.What potential difference across the plates is required to store 7.2 x 10-4 C on this capacitor?

Find the electrical potential at 0.15 m from a point charge of 6.0 mC.(ke = 8.99 x 109 N*m2/C2)

A point charge of +3.0 mC is located at the origin of a coordinate system and a second point charge of -6.0 mC is at x = 1.0 m.At what point on the x axis is the electrical potential zero?

Electrons in an x-ray machine are accelerated from rest through a potential difference of 50 000 V.What is the kinetic energy of each of these electrons in eV?

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 x 10-19 J)

If a doubly-ionized oxygen atom (O-2) is accelerated from rest by going through a potential difference of 20 V,what will be the change in its kinetic energy?

A solid conducting sphere of 10 cm radius has a net charge of 20 nC.If the potential at infinity is taken as zero,what is the potential at the center of the sphere?

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 +3.4 and +6.6 mC are separated by 0.10 m.What is the electrical potential at the point midway between the two point charges? (ke = 8.99 x 109 N*m2/C2)

The unit of capacitance,the farad,is dimensionally equivalent to which of the following?

A point charge of +3.0 mC is located at the origin of a coordinate system and a second point charge of -6.0 mC is at x = 1.00 m.What is the electric potential at the x = 0.50 m point? (ke = 8.99 x 109 N*m2/C2)

Two protons,each of charge 1.60 x 10-19 C,are 2.00 x 10-5 m apart.What is the change in potential energy if they are brought 1.00 x 10-5 m closer together? (ke = 8.99 x 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?

At which location will the electric field between the two parallel plates of a charged capacitor be the strongest in magnitude?

At what distance from a point charge of 8.0 mC would the electrical potential be 4.2 x 10⁴ V? (k_e = 8.99 x 10⁹ N*m²/C²)

Two point charges of values +3.4 and +6.6 mC,respectively,are separated by 0.20 m.What is the potential energy of this 2-charge system? (k_e = 8.99 x 10⁹ N*m²/C²)

A parallel-plate capacitor has a capacitance of 20 µF.What potential difference across the plates is required to store 7.2 x 10^-4 C on this capacitor?

Find the electrical potential at 0.15 m from a point charge of 6.0 mC.(k_e = 8.99 x 10⁹ N*m²/C²)

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 x 10^-19J)

If a doubly-ionized oxygen atom (O^-²) is accelerated from rest by going through a potential difference of 20 V,what will be the change in its kinetic energy?

Two point charges of values +3.4 and +6.6 mC are separated by 0.10 m.What is the electrical potential at the point midway between the two point charges? (k_e = 8.99 x 10⁹N*m²/C²)

A point charge of +3.0 mC is located at the origin of a coordinate system and a second point charge of -6.0 mC is at x = 1.00 m.What is the electric potential at the x = 0.50 m point? (k_e = 8.99 x 10⁹ N*m²/C²)

Two protons,each of charge 1.60 x 10^-19 C,are 2.00 x 10^-5 m apart.What is the change in potential energy if they are brought 1.00 x 10^-5 m closer together? (k_e = 8.99 x 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?