Question

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 20.0 cm, giving it a charge of -12.0 μC. Part A: Find the electric field just inside the paint layer
Part B: Find the electric field just outside the paint layer
Part C: Find the electric field 6.00 cm outside the surface of the paint layer

Answer 1

Answer:

(a) 0 N/C

(b) - 2.7 x 10^6 N/C

(c) - 1.6 x 10^6 N/C

Explanation:

q = -12 micro Coulomb

(a) According to the Gauss's theorem

$\int E.ds=\frac{q_{enclosed}}{\epsilon _{0}}$

Here, E be the electric field, ds be the area of gaussian surface and q be the charge enclosed.

In this case, the charge enclosed is zero, so the electric field is zero.

E = 0

(b) r = 20 cm = 0.2 m

Use the formula for the electric field

$E = \frac{1}{4\pi \epsilon _{0}}\times \frac{q}{r^{2}}$

$E = -\frac{9\times 10^{9}\times 12\times 10^{-6}}{0.2\times 0.2}$

E = - 2.7 x 10^6 N/C

(c) r = 20 + 6 = 26 cm = 0.26 m

Use the formula for the electric field

$E = \frac{1}{4\pi \epsilon _{0}}\times \frac{q}{r^{2}}$

$E = -\frac{9\times 10^{9}\times 12\times 10^{-6}}{0.26\times 0.26}$

E = - 1.6 x 10^6 N/C