What is the potential difference

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Assignment Problem: Electric Potential Questions

Section 1: Potential Difference and Potential near a Charged Sheet

Question 1: Let A = (x₁, y₁) and B = (x₂, y₂) be two points near and on the same side of a charged sheet with surface charge density +σ. The electric field E→ due to such a charged sheet has magnitude E = σ/2∈₀ everywhere, and the field points away from the sheet, as shown in the diagram.

Part A: What is the potential difference V_AB = V_A - V_B between points A and B?

Question 2: At a certain distance from a point charge, the potential and electric field magnitude due to that charge are 4.98 V and 12.0 V/m, respectively. (Take the potential to be zero at infinity.)

Part A: What is the distance to the point charge?

Part B: What is the magnitude of the charge?

Part C: Is the electric field directed toward or away from the point charge?

Question 3: Two point charges q₁ = 2.30 nC and q₂ = -6.80 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q1 and 0.060 m from q₂ (the figure). Take the electric potential to be zero at infinity.

Part A - Find the potential at point A.

Part B - Find the potential at point B.

Part C - Find the work done by the electric field on a charge of 2.50 nC that travels from point B to point A.

Question 4: Two large parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20 cm.

Part A - If the surface charge density for each plate has magnitude 47.0 nC/m², what is the magnitude of E→ in the region between the plates?

Part B - What is the potential difference between the two plates?

Part C - If the separation between the plates is doubled while the surface charge density is kept constant at the value in part (a), what happens to the magnitude of the electric field?

- doubles

- stays the same

- halves

Part D: If the separation between the plates is doubled while the surface charge density is kept constant at the value in part (a), what happens to the potential difference?

- doubles

- stays the same

- halves

Question 5: A total electric charge of 3.50 nC is distributed uniformly over the surface of a metal sphere with a radius of 18.0 cm. The potential is zero at a point at infinity.

Part A - Find the value of the potential at 55.0 cm from the center of the sphere.

Part B - Find the value of the potential at 18.0 cm from the center of the sphere.

Part C - Find the value of the potential at 17.0 cm from the center of the sphere.

Section 2: Electric Potential, Potential Energy, and Force

Learning Goal: To review relationships among electric potential, electric potential energy, and force on a test charge.

Question 1: This question is a review of the relationship between an electric field E→, its associated electric potential V, the electric potential energy U, and the direction of force on a test charge.

Part A: Electric field lines always begin at _______ charges (or at infinity) and end at _______ charges (or at infinity). One could also say that the lines we use to represent an electric field indicate the direction in which a _______ test charge would initially move when released from rest. Which of the following fills in the three missing words correctly?

(positive; negative; negative)

(positive; negative; positive)

(negative; positive; negative)

(negative; positive; positive)

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