Question

in the figure, charges at A and B are kept fixed . The value of x for which coulomb force experience d by charge C wil be maximum, is
figure is in image and plz give correct answer ​

Answer 1

Magnitude of force will be maximum at both x = ±a/sqrt(2) but directions will be opposite. In this question, x is assumed to be above the line joining A to B. So, x = +a/sqrt(2).

Also, magnitude of force will be minimum if x = 0.

Hope, this helps...

Answer 2

Answer:

The value of x for which coulomb force experienced by charge C will be maximum, is a/√2.

Explanation:

Given,

Three charges of magnitude "Q" are placed at points 'A', 'B', 'C'.

To find,

The perpendicular value "x" from the line joining A, B to C.

Calculation,

let 'F' be the force between the charges AC and BC.

Let the angle ∠ACB be 2β. And the length of side AC = BC = d.

Then by resolving the force 'F' into vertical and horizontal components results in:

Due to charges AC :                              Due to charges BC :

F cos(β) in the upward direction.          F cos(β) in the upward direction.

F sin(β) along the direction AB.             F sin(β) along the direction BA.

Hence, F sin(β) due to charges AC and F sin(β) due to charges BC gets cancelled out. As, they are in opposite direction.

And F cos(β) due to charges AC and F cos(β) due to charges BC gets added up in the vertically upward direction.

So the net resultant force $F_{net} = 2F \cos(\beta)$.

     $\implies F_{net} = \frac{2\times KQ^2}{d^2} \times \frac{x}{d}$    (As form the figure cos(β) = x/d)

    $\implies F_{net} = \frac{2\times KQ^2}{(\sqrt{x^2 + a^2} )^2} \times \frac{x}{\sqrt{x^2+a^2} }$  (Since $d = \sqrt{x^2 + a^2}$)

    $\implies F_{net} = 2\times KQ^2\times \frac{x}{(\sqrt{x^2 + a^2} )^\frac{3}{2} }$

For maximum condition $F_{net}' = 0$ i.e. first derivative is zero.

$F_{net}' = 2KQ^2\times \frac{x\times \frac{3}{2} (\sqrt{{x^2+a^2} }) \times 2x -(x^2 +a^2)^\frac{3}{2}\times 1 }{(x^2+a^2)^3} = 0$

           $\implies x = \pm \frac{a}{\sqrt{2} }$

Therefore, the value of x for which coulomb force experienced by charge C will be maximum, is a/√2.

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