First slide

Magnetism

Question

The force between the two poles is reduced to $' x'$ newton, when their separation is increased to n times. From this value, it increases by ‘y’ newtons when their separation made $\frac{1}{n} t h$ of their original value. The relation between x and y is

Moderate

A

$x = y (n^{4} - 1)$
B

$x = n^{4} y$
C

$y = (1 - n^{4}) x$
D

$y = (n^{4} - 1) x$

Solution

$W e k n o w, F = \frac{μ_{0}}{4 π} \frac{m_{1} m_{2}}{r^{2}} \Rightarrow F \propto \frac{1}{r^{2}}$
$I n i t i a l l y, x \propto \frac{1}{n^{2}} . . . . . . . (1); F i n a l l y, x + y \propto \frac{1}{{(\frac{1}{n})}^{2}} . . . . . . (2);$
$D i v i d i n g, \frac{(1)}{(2)} \Rightarrow \frac{x}{x + y} = \frac{1}{n^{4}}$
$\Rightarrow x + y = (n^{4}) x \Rightarrow y = n^{4} x - x = x (n^{4} - 1)$

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