JEE MAIN - Physics (2016 - 9th April Morning Slot - No. 13)
A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75o. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30o with this field. The magnitude of the other field (in mT ) is close to
11
36
1
1060
Explanation
For equilibrium,
net torque acting on dipole is = 0
$$ \therefore $$ $$\tau $$1 = $$\tau $$2
$$ \Rightarrow $$ mB1 sin$$\theta $$1 = mB2 sin$$\theta $$2
$$ \Rightarrow $$ B2 = B1 $$ \times $$ $${{\sin {{30}^o}} \over {\sin {{45}^o}}}$$
= 15 $$ \times $$ $$\sqrt 2 $$ $$ \times $$ $${1 \over 2}$$ =
= 10.6 mT $$ \simeq $$ 11 mT
net torque acting on dipole is = 0
$$ \therefore $$ $$\tau $$1 = $$\tau $$2
$$ \Rightarrow $$ mB1 sin$$\theta $$1 = mB2 sin$$\theta $$2
$$ \Rightarrow $$ B2 = B1 $$ \times $$ $${{\sin {{30}^o}} \over {\sin {{45}^o}}}$$
= 15 $$ \times $$ $$\sqrt 2 $$ $$ \times $$ $${1 \over 2}$$ =
= 10.6 mT $$ \simeq $$ 11 mT
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