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

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

Answer 2

The electric field is the field in the space, where the charge is present, and exerts the force on all other charged particles.

The number of excess electron must be distributed uniformly within the volume of an isolated plastic sphere required is $1.622\times10^{10}$.

What is uniform electric field?

The electric field is the field in the space, where the charge is present, and exerts the force on all other charged particles.

It can be given as,

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

Here, $k$ is the Coulomb's constant $q$ is the charge of the object and the $r$is the distance.

Given information-

The diameter of the plastic sphere is 25.0 cm.

The value of electric field is 1500 N/C.

Put the values in the above formulas as,

$1500=\dfrac{9\times10^9q}{(0.025)^2}\\q=2.36\times10^9\rm C$

The number of electron is the ratio of total charge to the charge on one electron. Thus the number of electron required is,

$n=\dfrac{2.6\times10^{9}}{1.602\times10^{-19}} \\n=1.622\times10^{10}$

Thus the number of excess electron must be distributed uniformly within the volume of an isolated plastic sphere required is $1.622\times10^{10}$.

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