Electric Fields with Calculus Video Lessons

Concept

Problem: Two 10-cm-diameter charged rings face each other, 29 cm apart. The left ring is charged to -27 nC and the right ring is charged to +27 nC .Part A. What is the magnitude of the electric field E at the midpoint between the two rings? Express your answer to two significant figures and include the appropriate units.Part B. What is the direction of the electric field E at the midpoint between the two rings?a) Toward the right ring.b) Toward the left ring.c) Parallel to the plane of the rings.Part C. What is the magnitude of the force F on a -1.0 nC charge placed at the midpoint? Express your answer to two significant figures and include the appropriate units.Part D. What is the direction of the force F on a -1.0 nC charge placed at the midpoint?a) Parallel to the plane of the rings.b) Toward the left ring.c) Toward the right ring.

FREE Expert Solution

Part A

Electric field, E:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{Q}}{{\mathbf{r}}^{\mathbf{2}}}}$

At the midpoint between the rings, E is:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{Q}\mathbf{x}}{{\mathbf{\left(}\mathbf{r}\mathbf{2}\mathbf{+}\mathbf{x}\mathbf{2}\mathbf{\right)}}^{\mathbf{3}}{\mathbf{2}}}}}$

r = D/2 = 10/2 = 5 cm = 0.05 m

x = 29/2 = 14.5 cm = 0.145 m

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Problem Details

Two 10-cm-diameter charged rings face each other, 29 cm apart. The left ring is charged to -27 nC and the right ring is charged to +27 nC .

Part A. What is the magnitude of the electric field E at the midpoint between the two rings? Express your answer to two significant figures and include the appropriate units.

Part B. What is the direction of the electric field at the midpoint between the two rings?

a) Toward the right ring.

b) Toward the left ring.

c) Parallel to the plane of the rings.

Part C. What is the magnitude of the force F on a -1.0 nC charge placed at the midpoint? Express your answer to two significant figures and include the appropriate units.

Part D. What is the direction of the force F on a -1.0 nC charge placed at the midpoint?

a) Parallel to the plane of the rings.

b) Toward the left ring.

c) Toward the right ring.