First slide

Magnetism

Question

When a bar magnet is placed at $90^{0}$ to a uniform magnetic field. It is acted upon by a couples which is maximum. For the couple to be half of the maximum value at what angle should the magnet be inclined to the magnetic field B

Moderate

A

$30^{0}$
B

$45^{0}$
C

$60^{0}$
D

$90^{0}$

Solution

We know $τ = M B \sin θ$
If $θ = 90^{0}$
$t h e n, τ_{\max} = M B L e t s a y a t a n g l e t h a t θ, m a x t o r q u e b e c o m e s h a l f, \Rightarrow \frac{1}{2} τ_{\max} = M B \sin θ$
$\begin{array}{l} \Rightarrow \frac{M B}{2} = M B \sin θ \\ \Rightarrow \sin θ = \frac{1}{2} \end{array}$
$\begin{array}{l} \Rightarrow \sin θ = \sin 30 ° \\ \Rightarrow θ = 30 ° \end{array}$

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