Question

Two magnets have moments are in the ratio X: Y and their lengths in the ratio X : Z. The ratio of pole strength is

Answer 1

Explanation:

M=ml

M1/M2=m1/m2×l1/l2

M1/M2×l2/l1=m1/m2

X/Y×Z/X=m1/m2

m1/m2=Z:Y

Answer 2

Answer:

The ratio of pole strengths of two magnets is  Z:Y.

Explanation:

Given the ratio of magnetic moments of two magnets is  X:Y

                           i.e., $\frac{m_{1} }{m_{2}} =\frac{X}{Y}$

          the ratio of lengths of two magnets is X:Z

                           i.e., $\frac{l_{1} }{l_{2}} =\frac{X}{Z}$

The pole strength(p) of a magnet is given by the ratio of magnetic moment(m) of the magnet to the length(l) of magnet.

i.e., $p=\frac{m}{l}$

Ratio of pole strengths is

$\frac{p_{1} }{p_{2}} =\frac{\frac{m_{1} }{l_{1} }}{\frac{m_{2} }{l_{2} }}$

   $={\frac{m_{1} }{l_{1} }} \times {\frac{l_{2} }{m_{2} }}$

   $={\frac{m_{1} }{m_{2} }} \times {\frac{l_{2} }{l_{1} }}$

   $={\frac{X }{Y }} \times {\frac{Z}{X }}$

   $={\frac{Z }{Y }}$

Therefore, the ratio of pole strengths of two magnets is  ${\frac{Z }{Y }}$ or Z:Y.