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Question: The magnetic field at a point X on the axis of a small bar magnet is equal to the field at a point Y...

The magnetic field at a point X on the axis of a small bar magnet is equal to the field at a point Y on the equator of the same magnet. The ratio of the distance of X and Y from the centre of the magnet is

A

2−32 ^ { - 3 }

B

2−1/32 ^ { - 1 / 3 }

C

232 ^ { 3 }

D

21/32 ^ { 1 / 3 }

Answer

21/32 ^ { 1 / 3 }

Explanation

Solution

Suppose distances of points X and Y from magnet are x and y respectively then According to question Baxial =Bequatorial B _ { \text {axial } } = B _ { \text {equatorial } }

⇒ μ04π⋅2Mx3=μ04π⋅My3⇒xy=21/31\frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 M } { x ^ { 3 } } = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { M } { y ^ { 3 } } \Rightarrow \frac { x } { y } = \frac { 2 ^ { 1 / 3 } } { 1 }