Question

Two concentric circular coils of ten turns each are situated in the same plane. Their radii are 20 and 40 cm and they carry respectively 0.2 and 0.3 ampere current in opposite direction. The magnetic field in weber / m² at the centre is

• A. $\frac { 35 } { 4 } \mu _ { 0 }$
• B. $\frac { \mu _ { 0 } } { 80 }$
• C. $\frac { 7 } { 80 } \mu _ { 0 }$
• D. $\frac { 5 } { 4 } \mu _ { 0 }$

Answer 1

Answer: (D)

$\frac { 5 } { 4 } \mu _ { 0 }$

Answer 2

Two coils carrying current in opposite direction, hence net magnetic field at centre will be difference of the two fields.

i.e. $B _ { n e t } = \frac { \mu _ { 0 } } { 4 \pi } \cdot 2 \pi N \left[ \frac { N i _ { 1 } } { r _ { 1 } } - \frac { i _ { 2 } } { r _ { 2 } } \right]$ $= \frac { 10 \mu _ { 0 } } { 2 } \left[ \frac { 0.2 } { 0.2 } - \frac { 0.3 } { 0.4 } \right] = \frac { 5 } { 4 } \mu _ { 0 }$