If some charge is given to a solid metallic sphere, the field ins… - Vidyadip

MCQ

If some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss's law all the charge resides on the surface. Now, suppose that Coulomb's force between two charges varies as $1 / r^{3}$. Then, for a charged solid metallic sphere

A
field inside will be zero and charge density inside will be zero
B
field inside will not be zero and charge density inside will not be zero
C
field inside will not be zero and charge density inside will be zero
✓
field inside will be zero and charge density inside will not be zero

✓

Answer

Correct option: D.

field inside will be zero and charge density inside will not be zero

d
$(d)$ As Coulomb's force,

$\quad F \propto \frac{1}{r^{3}}$

$\Rightarrow \text { Electric field, } E \propto \frac{1}{r^{3}} \Rightarrow E=\frac{k q}{r^{3}}$

Now, for Gaussian surface $(r < R)$.

Electric flux linked with surface is

$\phi=\int \frac{k q}{r^{3}} \cdot 2 \pi r d r$

$=2 \pi k q \int \frac{d r}{r^{2}}=2 \pi k q\left(-\frac{1}{r}\right)$

As flux is non-zero, charge density is also non-zero. Also, by symmetry of charge distribution electric field is zero.

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