Question

Two circular coils X and Y have equal number of turn and carry equal currents in the same sense and subtend same solid angle at point O. If the smaller coil X is midway between O and Y , then if we represent the magnetic induction due to bigger coil Y at O as B_Y and that due to smaller coil X at O B_x, then:

• A. $\frac { B _ { Y } } { B _ { X } }$ = 1
• B. $\frac { B _ { Y } } { B _ { X } }$ = 2
• C. $\frac { B _ { Y } } { B _ { X } }$ = $\frac { 1 } { 2 }$
• D. $\frac { 1 } { 4 }$

Answer 1

Answer: (C)

$\frac { B _ { Y } } { B _ { X } }$ = $\frac { 1 } { 2 }$

Answer 2

As two coils subtend the same solid angle at O, hence area of coil, Y = 4 × area of coil

i.e. radius of coil Y = 2 × radius of coil X

\B_Y = $\frac { \mu _ { 0 } } { 4 \pi }$ × $\frac { 2 \pi \mathrm { I } ( \mathrm { r } ) ^ { 2 } } { \left[ \mathrm { r } ^ { 2 } + \left( \frac { \mathrm { d } } { 2 } \right) ^ { 2 } \right] ^ { 3 / 2 } }$

\ $\frac { 4 } { ( 4 ) ^ { 3 / 2 } }$ = $\frac { 4 } { 8 }$

= $\frac { 1 } { 2 }$