**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:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{Q}\mathbf{x}}{{\mathbf{(}\mathbf{r}\mathbf{2}\mathbf{+}\mathbf{x}\mathbf{2}\mathbf{)}}^{{\displaystyle \raisebox{1ex}{$\mathbf{3}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}}}}$

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

x = 29/2 = 14.5 cm = 0.145 m

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.

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