Question

Which of the following is not true about the electric field intensity E⃗ of a uniformly charged solid sphere?

a. E⃗ is maximum at the surface of the sphere

b. E⃗ is directly proportional to the distance from the centre of the sphere

c. E⃗ decreases as a square of the distance from the surface of the sphere

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

Answer 1

Question #31258, Physics, Other

Which of the following is not true about the electric field intensity $E^{+}$ of a uniformly charged solid sphere?

a. $E^{+}$ is maximum at the surface of the sphere

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

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

d. $E^{+}$ 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 sphere radius $R$ (b is true).

$$E _ {r} = \frac {1}{4 \pi \varepsilon_ {0}} \frac {Q}{R ^ {3}} r$$

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 surface of the sphere $(r > R)$ - c is true;

$$E _ {r} = \frac {1}{4 \pi \varepsilon_ {0}} \frac {Q}{r ^ {2}}$$

But $E_{r}$ not decreases as a square of the distance from the centre of the sphere, so $\mathbf{d}$ is not true.

Answer: d. $E_{r}$ decreases as a square of the distance from the centre of the sphere – is not true.