Question

How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 25.0 cm in diameter to produce an electric field of 1500 N/C just outside the surface of the sphere?

Answer 1

Answer:

Required charge $q=2.6\times 10^{9}C$.

$n=1.622\times 10^{10}\ electrons$

Explanation:

Given:

Diameter of the isolated plastic sphere = 25.0 cm

Magnitude of the Electric field = 1500 N/C

now

Electric field (E) is given as:

$E =\frac{kq}{r^2}$

where,

k = coulomb's constant = 9 × 10⁹ N

q = required charge

r = distance of the point from the charge where electric field is being measured

The value of r at the just outside of the sphere = $\frac{25.0}{2}=12.5cm=0.125m$

thus, according to the given data

$1500N/C=\frac{9\times 10^{9}N\times q}{(0.125m)^2}$

or

$q=\frac{0.125^2\times 1500}{9\times 10^{9}}$

or

Required charge $q=2.6\times 10^{9}C$.

Now,

the number of electrons (n) required will be

$n=\frac{required\ charge}{charge\ of\ electron}$

or

$n=\frac{2.6\times 10^{-9}}{1.602\times 10^{-19}}$

or

$n=1.622\times 10^{10}\ electrons$