A certain charge Q is divided into parts q and (Q – q). How should the charges Q and q be divided so that q and (Q – q) placed at a certain distance apart experience maximum electrostatic repulsion?

Option 1 - <math> <mrow> <mi>Q</mi> <mo>=</mo> <mfrac> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>

Option 2 - <math> <mrow> <mi>Q</mi> <mo>=</mo> <mn>4</mn> <mi>q</mi> </mrow> </math>

Option 3 - <math> <mrow> <mi>Q</mi> <mo>=</mo> <mn>2</mn> <mi>q</mi> </mrow> </math>

Option 4 - Q = 3q

3 Views|Posted 6 months ago

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Alok Kumar Singh | Contributor-Level 10

6 months ago

Correct Option - 3

Detailed Solution:

$F = \frac{q (Q - q)}{4 π ε_{0} r^{2}} \Rightarrow \frac{d F}{d q} = \frac{1}{4 π ε_{0} r^{2}} (Q - 2 q) \Rightarrow \frac{d F}{d q} = \frac{1}{2 π ε_{0} r^{2}}$

Here r is fixed

For maxima or minima of force, its first derivative should be zero.

$\frac{d F}{d q} = \frac{1}{4 π ε_{0} r^{2}} (Q - 2 q) = 0 \Rightarrow q = \frac{Q}{2}$

Since second derivative is always negative so maxima will occur at this value of q.

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