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Question: A circular loop of radius 3 cm is having a current of 12.5 A. The magnitude of magnetic field at a d...

A circular loop of radius 3 cm is having a current of 12.5 A. The magnitude of magnetic field at a distance of 4 cm on its axis is

A

5.65 × 10-5 T

B

5.27 × 10-5 T

C

6.54 × 10-5 T

D

9.20 × 10-5 T

Answer

5.65 × 10-5 T

Explanation

Solution

Here,I=12.5 A,R=3 cm=3×10−2 m\mathrm { I } = 12.5 \mathrm {~A} , \mathrm { R } = 3 \mathrm {~cm} = 3 \times 10 ^ { - 2 } \mathrm {~m}

X= 4 cm = 4×10−2 m4 \times 10 ^ { - 2 } \mathrm {~m}

∴B=4π×10−7×12.5×(3×10−2)22[(3×10−2)2+(4×10−2)2]3/2=5.65×10−5 T\therefore B = \frac { 4 \pi \times 10 ^ { - 7 } \times 12.5 \times \left( 3 \times 10 ^ { - 2 } \right) ^ { 2 } } { 2 \left[ \left( 3 \times 10 ^ { - 2 } \right) ^ { 2 } + \left( 4 \times 10 ^ { - 2 } \right) ^ { 2 } \right] ^ { 3 / 2 } } = 5.65 \times 10 ^ { - 5 } \mathrm {~T}