Question

12) Which of the following is NOT true about the electric field intensity
E⃗
E→
of a uniformly charged solid sphere?
a) E⃗
E→
is maximum at the surface of the sphere

b) E⃗
E→
is directly proportional to the distance from the centre of the sphere

c) E⃗
E→
decreases as a square of the distance from the surface of the sphere

d) E⃗
E→
decreases as a square of the distance from the centre of the sphere.

Answer 1

Answer on Question #61331-Physics-Electromagnetism

12) Which of the following is not true about the electric field intensity $\vec{E}$ of a uniformly charged solid sphere?

a. $\vec{E}$ is maximum at the surface of the sphere

b. $\vec{E}$ is directly proportional to the distance from the centre of the sphere

c. $\vec{E}$ decreases as a square of the distance from the surface of the sphere

d. $\vec{E}$ decreases as a square of the distance from the centre of the sphere.

Solution

Electric field intensity $E(r)$ of a uniformly charged solid sphere is directly proportional to the distance from the centre of the sphere, when this distance $r$ less than the sphere radius $R$ (b. is true).

$$E(r) = \frac{Q}{4\pi\varepsilon_0} \frac{r}{R^3},$$

where $Q$ is the total charge.

Also $E(r)$ is maximum at the surface of the sphere (a. is true).

And $E(r)$ decreases as a square of the distance from the centre of the sphere ($r > R$) (d. is true).

$$E(r) = \frac{Q}{4\pi\varepsilon_0} \frac{1}{r^2}.$$

But $E(r)$ doesn't decrease as a square of the distance from the surface of the sphere (c is not true).

Answer: c.

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