Question

7) Use Gauss' Law to solve this problem. A 6 nC (nanocoulomb) charge is located at the center of a 2 meter radius uncharged spherical metal shell. Calc. the electric field at a radius of r 1 meter in N/C. (a) 14 (b) 24 (c) 34 (d) 54 8) An electric field is 4 X 10 v/m at an angle of 30 to the x axis. A charge undergoes a displacement vector of 3 m j. (3 meters along the y axis). Calc. the potential difference in volts. (a) 6 X 10% (b) 8 x 10% (c)1x 10 (d) 1.2x 10

Answer 1

(7)

Integral form

$\oint\vec{E}\cdot d\vec{a}=\frac{Q_{enc.}}{\epsilon_0}$

Due to spherical symmetry, we have

$E(4\pi r^2)=\frac{Q_{enc.}}{\epsilon_0}$

Therefore,

$E=\frac{9\times10^9\times6\times10^{-9}}{1}=54\textup{ N/C}$

(8)

$V=\int\vec{E}\cdot d\vec{S}$

$\vec{E}=4\times10^5\left (\cos30\hat{\imath}+\sin30\hat{\jmath} \right ),\ \vec{S}=3\,\hat{\jmath}$

Thus,

$V=6\times10^5\textup{ V}$