Question

For the given arrangement, a fixed finite line charge is kept in front of a block at equilibrium having $-10\text{nC}$ charge on it. Block and finite line charge are along same line. If in equilibrium, extension of spring is $10\text{cm}$ then spring constant $\left(K\right)$ is

• A. $3000\text{N/m}$
• B. $3500\text{N/m}$
• C. $3375\text{N/m}$
• D. $2575\text{N/m}$

Answer 1

The correct option is C $3375\text{N/m}$

Electrostatic force $F$ at position of block in equilibrium due to line charge is
$F=Kq\lambda [\frac{1}{a}-\frac{1}{a+L}]$
Given:
$a=2\text{m}$
$L=6\text{m}$
$\lambda =10\text{C/m}$
$q=-10\text{nC}$
$x=10\text{cm}$
$\Rightarrow F=9\times {10}^9\times 10\times {10}^{-9}\times 10\times [\frac{1}{2}-\frac{1}{2+6}]$
$\Rightarrow F=337.5\text{N}$ ... (1)
Now, at equilibrium, $F=Kx$
$\Rightarrow K=\frac{F}{x}$
$\Rightarrow K=\frac{337.5}{10\times {10}^{-2}}$
$\Rightarrow K=3375\text{N/m}$