Question

Column- I gives some current distributions and a point P in the space around these current distributions. Column II gives some expressions of magnetic field strength. Match column- I to corresponding field strength at point P given in Column - II.
$\begin{array}{cccc}& \text{Column I}& & \text{Column - II}\\ \text{(A)}& \text{A conducting loop shaped as regular hexagon of side}x\text{,}& \text{(P)}& \frac{3{\mu }_{0}i}{32\pi x}\\ & \text{carrying current i. P is the centriod of hexagon}& & \\ \text{(B)}& \text{A cylinder of inner radius}x\text{and outer radius}3x\text{, carrying}& \text{(Q)}& \frac{\sqrt{3}{\mu }_{0}i}{\pi x}\\ & \text{current i. Point P is at a distance}2x\text{from the axis of the cylinder}& & \\ & \text{the cylinder}& & \\ \text{(C)}& \text{Two coaxial hollow cylinders of radii}x\text{and}2x\text{, each carrying}& \text{(R)}& \frac{{\mu }_{0}i}{2x}\\ & \text{current i, but in opposite direction. P is a point at distance}& & \\ & 1.5x\text{from the axis of the cylinders}& & \\ \text{(D)}& \text{Magnitude field at the centre of an n-sided regular}& \text{(S)}& \frac{{\mu }_{0}i}{3\pi x}\\ & \text{polygon of circum circle of radius}x\text{, carrying current}& & \\ & \text{i,}\text{take}n\to \infty ,\text{P is centroid of the polygon}& \text{(T)}& \text{Zero}\end{array}$

• A. $\left(A\right)\to \left(Q\right);\left(B\right)\to \left(P\right);\left(C\right)\to \left(S\right);\left(D\right)\to \left(R\right)$
• B. $\left(A\right)\to \left(Q\right);\left(B\right)\to \left(T\right);\left(C\right)\to \left(S\right);\left(D\right)\to \left(P\right)$
• C. $\left(A\right)\to \left(T\right);\left(B\right)\to \left(P\right);\left(C\right)\to \left(Q\right);\left(D\right)\to \left(S\right)$
• D. $\left(A\right)\to \left(R\right);\left(B\right)\to \left(S\right);\left(C\right)\to \left(Q\right);\left(D\right)\to \left(P\right)$

Answer 1

The correct option is A $\left(A\right)\to \left(Q\right);\left(B\right)\to \left(P\right);\left(C\right)\to \left(S\right);\left(D\right)\to \left(R\right)$

For A ;$B_p=6\times \frac{{\mu }_{0}i}{4\pi \left(x\sin {60}^{\circ }\right)}[\sin {30}^{\circ }+\sin {30}^{\circ }]B_p=\frac{\sqrt{3}{\mu }_{0}i}{\pi x}$

For B ; $B_p=\frac{{\mu }_0\left(\frac{3}{8}i\right)}{2\pi \left(2x\right)}=\frac{3{\mu }_{0}i}{32\pi x}$

For C : $B_p=\frac{{\mu }_{0}i}{2\pi \left(1.5x\right)}=\frac{{\mu }_{0}i}{3\pi x}$

For D : If $n\to \infty$, n sided polygon $\to$ circle so $B=\frac{{\mu }_{0}i}{2x}$