Question

What mass of a point charge kept above finite line charge at axial line can be balanced by the electric field produced by finite line charge.

• A. $0.6\times {10}^{-7}\text{kg}$
• B. $1.6\times {10}^{-7}\text{kg}$
• C. $2.6\times {10}^{-7}\text{kg}$
• D. $3.6\times {10}^{-7}\text{kg}$

Answer 1

The correct option is B $1.6\times {10}^{-7}\text{kg}$

$E$ at position of mass in state of equilibrium due to line charge is
$E=K\lambda [\frac{1}{r}-\frac{1}{r+L}]$
Given:
$r=0.5\text{m}$
$L=5\text{m}$
$\lambda =10\text{nC/m}$
$q=10\text{nC}$
$m=?$
From equilibrium of forces,
$F=mg$
$\Rightarrow qE=mg$
$\Rightarrow E=\frac{mg}{q}$
$\Rightarrow K\lambda [\frac{1}{r}-\frac{1}{r+L}]=\frac{mg}{q}$
$\Rightarrow 9\times {10}^9\times 10\times {10}^{-9}[\frac{1}{0.5}-\frac{1}{0.5+5}]=\frac{m\times 10}{10\times {10}^{-9}}$
$\Rightarrow m=1.6\times {10}^{-7}\text{kg}$