Question

The magnetic field B due to a current carrying circular loop of radius 12 cm at its centre is0.5 × 10^–4 T. The magnetic field due to this loop at a point on the axis at a distance of 5 cm from the centre-

• A. 3.9 × 10^–5 T
• B. 5.2 × 10^–5 T
• C. 2.1 × 10^–5 T
• D. 9 × 10^–5 T

Answer 1

Answer: (A)

3.9 × 10^–5 T

Answer 2

B₀ = $\frac { \mu _ { 0 } I } { 2 \mathrm { a } }$ At axial point

B = $\frac { \mu _ { 0 } \mathrm { Ia } ^ { 2 } } { 2 \left( \mathrm { a } ^ { 2 } + \mathrm { x } ^ { 2 } \right) ^ { 3 / 2 } }$ = $\frac { a ^ { 3 } } { \left( a ^ { 2 } + x ^ { 2 } \right) ^ { 3 / 2 } }$

Ž B = B₀ $\frac { a ^ { 3 } } { \left( a ^ { 2 } + x ^ { 2 } \right) ^ { 3 / 2 } }$

= 0.5 × 10^–4 × $\frac { ( 12 \mathrm {~cm} ) ^ { 3 } } { \left( 144 \mathrm {~cm} ^ { 2 } + 25 \mathrm {~cm} ^ { 2 } \right) ^ { 3 / 2 } }$ = 3.9 × 10^–5 T.