Magnetics 6 Question 12
12. Statement I The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
(2008, 3M)
Statement II Soft iron has a high magnetic permeability and cannot be easily magnetised or demagnetised.
Analytical & Descriptive Questions
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Solution:
- Key Idea Net force experienced by two wires separated by same distance is attractive, if current flow in them in same direction. However, this force is repulsive in nature, if current in them flows in opposite direction.
Force on a wire 1 in which current $I _1$ is flowing due to another wire 2 which are separated by a distance $r$ is given as
or
$$ \begin{aligned} & \mathbf{F}=I _1\left(l \times \mathbf{B} _2\right) \\ & F=\frac{\mu _0 I _1 I _2}{2 \pi r} \cdot l \sin \theta \quad \because \mathbf{B} _2=\frac{\mu _0 I _2}{2 \pi r} \end{aligned} $$
Thus, the given square loop can be drawn as shown below
$$ \begin{aligned} F _{A B} & =\frac{\mu _0 I _1}{2 \pi a} \cdot I _2 a(\text { away from wire } P Q) \\ F _{B C} & =F _{A D}=0 \quad\left[\because \theta=0^{\circ}\right] \\ F _{C D} & =\frac{\mu _0 I _1}{2 \pi(2 a)} \cdot I _2 a \\ & \left.=\frac{\mu _0 I _1}{4 \pi a} \cdot I _2 a \text { (towards the wire } P Q\right) \\ \therefore \quad F _{\text {net }} & =F _{A B}-F _{C D} \\ & =\frac{\mu _0 I _1 I _2}{2 \pi}-\frac{\mu _0 I _1 I _2}{4 \pi} \quad \text { (away from wire) } \\ & =\frac{\mu _0 I _1 I _2}{4 \pi} \quad \text { (repulsive in nature) } \end{aligned} $$
