Question

Find out the ratio of the currents through
two cta lor coils of radii 4cm and 16cm both
of which are eavivalent to mognete dipole
dipole
having eaval magnet moments.​

Answer 1

Explanation:

The magnetic field due to circular coil,

B1=2rμ0i=2(2π×10−2)μ0i1=4πμ0×3×102

B2=2(2π×10−2)μ0i2=4πμ0×4×102

B=B12+B22=4πμ0.5×102

⇒B=10−7×5×102⇒B=5×10−5Wb/m2

Answer 2

Answer:

The ratio of currents through the two coils is 16.

Explanation:

The magnetic moment of the coil is given,

$M=IA$           (1)

Where,

M=magnetic moment

I=current through the coil

A=area of the coil

From the question we have,

r₁=4cm=4×10⁻²m

r₂=16cm=16×10⁻²m

For the first coil we have,

$M_1=I_1\times \pi \times (4\times 10^-^2)^2$    (2)

And for the second coil we have,

$M_2=I_2\times \pi \times (16\times 10^-^2)^2$   (3)

From the question we have,

$M_1=M_2$    (4)

So,

$I_1\times \pi \times (4\times 10^-^2)^2=I_2\times \pi \times (16\times 10^-^2)^2$

$\frac{I_1}{I_2}=\frac{(16\times 10^-^2)^2}{(4\times 10^-^2)^2}$

$\frac{I_1}{I_2}=\frac{16\times 16}{4\times 4}=16$

Hence, the ratio of currents through the two coils is 16.