First slide

Applications involving charged particles moving in a magnetic field

Question

The tangent galvanometers having coils of the same radius are connected in series. A current flowing in them produces deflections of $60^{0}$ & $45^{0}$ respectively. The ratio of the number of turns in the coil is

Moderate

A

$4 / 3$
B

$(\sqrt{3} + 1) / 1$
C

$(\sqrt{3} + 1) / (\sqrt{3} - 1)$
D

$\sqrt{3} / 1$

Solution

In the first galvanometer $i_{1} = K_{1} \tan θ_{1}$
$i_{1} = K_{1} \tan 60^{0} = \sqrt{3} K_{1}$
In the second galvanometer $i_{2} = K_{2} \tan θ_{2}$
$i_{2} = K_{2} \tan 45^{0} = K_{2}$
In series combination $i_{1} = i_{2}$
$∴ \sqrt{3} K_{1} = K_{2} \Rightarrow \frac{K_{1}}{K_{2}} = \frac{1}{\sqrt{3}}$
But $K \propto \frac{1}{n}$
$\Rightarrow \frac{K_{1}}{K_{2}} = \frac{n_{2}}{n_{1}}$
$\Rightarrow \frac{n_{1}}{n_{2}} = \frac{K_{2}}{K_{1}} = \frac{\sqrt{3}}{1}$

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