The magnetic fields at two points on the axis of a circular coil at distance of 0.05 m and 0.2 m from the centre are in the ratio 8 :1 . The radius of the coil is

Question

The magnetic fields at two points on the axis of a circular coil at distance of 0.05 m and 0.2 m from the centre are in the ratio 8 :1 . The radius of the coil is (A) 0.2 m (B) 0.15 m (C) 0.1 m (D) 0.01 m.

Tardigrade Admin · Accepted Answer

(B1/B2) ((r2 + x22)3/2/(r2 + x12)3/2) i.e. (8/1) = ((r2 + 202)3/2/(r2 + 52)3/2) i.e. r = 0.1 m

Q. The magnetic fields at two points on the axis of a circular coil at distance of 0.05 m and 0.2 m from the centre are in the ratio 8 :1 . The radius of the coil is

0.2 m

0.15 m

0.1 m

0.01 m.

$\frac{B _{1}}{B _{2}} \frac{( r ^{2} + x _{2}^{2} ) ^{3/2}}{( r ^{2} + x _{1}^{2} ) ^{3/2}} i . e . \frac{8}{1} = \frac{( r ^{2} + 2 0 ^{2} ) ^{3/2}}{( r ^{2} + 5 ^{2} ) ^{3/2}} i . e . r$ = 0.1 m

Q. The magnetic fields at two points on the axis of a circular coil at distance of 0.05 m and 0.2 m from the centre are in the ratio 8 :1 . The radius of the coil is

0.2 m

0.15 m

0.1 m

0.01 m.

B2​B1​​(r2+x12​)3/2(r2+x22​)3/2​i.e.18​=(r2+52)3/2(r2+202)3/2​i.e.r = 0.1 m

$\frac{B _{1}}{B _{2}} \frac{( r ^{2} + x _{2}^{2} ) ^{3/2}}{( r ^{2} + x _{1}^{2} ) ^{3/2}} i . e . \frac{8}{1} = \frac{( r ^{2} + 2 0 ^{2} ) ^{3/2}}{( r ^{2} + 5 ^{2} ) ^{3/2}} i . e . r$ = 0.1 m