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STD 12 - 2. Electric potential and capacitance — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 - 2. Electric potential and capacitance4 Marks
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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