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 . 1. 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.2. What is the direction of the electric field E⃗  at the midpoint between the two rings?a. To the right ring. b. To the left ring. c. Parallel to the plane of the rings. 3. What is the magnitude of the force F⃗  on a -1.0 nC charge placed at the midpoint? Express your answer to two significant figures and include the appropriate units.4. What is the direction of the force F⃗  on a -1.0 nC charge placed at the midpoint?a. Parallel to the plane of the rings. b. To the left ring. c. To the right ring

###### FREE Expert Solution

This problem involves the electric field along the axis passing through the center of a ring.

The electric field is given by:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{Q}\mathbf{x}}{{\mathbf{\left(}\mathbf{x}\mathbf{2}\mathbf{+}\mathbf{a}\mathbf{2}\mathbf{\right)}}^{\mathbf{\left(}\mathbf{3}\mathbf{/}\mathbf{2}\mathbf{\right)}}}}$x is the distance from the ring, a is the radius of the ring.

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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 .

1. 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.

2. What is the direction of the electric field E⃗  at the midpoint between the two rings?

a. To the right ring.

b. To the left ring.

c. Parallel to the plane of the rings.

3. What is the magnitude of the force F⃗  on a -1.0 nC charge placed at the midpoint?

Express your answer to two significant figures and include the appropriate units.

4. What is the direction of the force F⃗  on a -1.0 nC charge placed at the midpoint?

a. Parallel to the plane of the rings.

b. To the left ring.

c. To the right ring