Magnetics 6 Question 11
11. A magnetic needle is kept in a non-uniform magnetic field. It experiences
(1982, 3M)
(a) a force and a torque
(b) a force but not a torque
(c) a torque but not a force
(d) neither a force nor a torque
Assertion and Reason
Mark your answer as
(a) If Statement I is true, Statement II is true; Statement II is the correct explanation for Statement I
(b) If Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
(c) If Statement I is true; Statement II is false
(d) If Statement I is false; Statement II is true
Show Answer
Solution:
- Given,
Area of the rectangular coil, $A=5 cm \times 2.5 cm$
$\Rightarrow \quad A=12.5 cm^{2}=12.5 \times 10^{-4} m^{2}$
Number of turns, $N=100$ turns
Current through the coil, $I=3 A$
Magnetic field applied, $B=1 T$
Angle between the magnetic field and area vector of the coil, $\theta=45^{\circ}$
As we know that, when a coil is tilted by an angle $\theta$ in the presence of some external magnetic field, then the net torque experienced by the coil is,
$$ \tau=\mathbf{M} \times \mathbf{B}=N I(\mathbf{A} \times \mathbf{B})=N I A B \sin \theta $$
Substituting the given values, we get
$$ \begin{aligned} \tau & =100 \times 3 \times 12.5 \times 10^{-4} \times 1 \times \sin 45^{\circ} \\ \tau & =0.707 \times 100 \times 3 \times 12.5 \times 10^{-4} N-m \\ & =2.651 \times 10^{-1} N-m \\ & \approx 0.27 N-m \end{aligned} $$
