Question

two circular coils of radius R and 2r carry current I and 2i respectively if magnetic induction at their centres are B1 and B2 then B1 divided by B2 is
1 is to1
1 is to 2
1 is to 4
2 is to 1

Answer 1

Answer:

B1=uo.i/2R

B2=uo.i/4R Ro=2R

B1/B2=2/1

2:1

option 4

Answer 2

Answer:

B₁ divided by B₂ is 1 is to 1 i.e. option (a).

Explanation:

The magnetic field induction for the circular current-carrying coil is given by,

$B=\frac{\mu_0I}{2R}$                  (1)

B= magnetic field induction

μ₀=permitivity of free space

I= current in the coil

R= radius of the coil

For First Coil

R₁=R

I₁=I

By putting these values in equation (1) we get;

$B_1=\frac{\mu_0 I}{2R}$                         (2)

For Second Coil

R₂=2R

I₂=2I

By putting these values in equation (1) we get;

$B_2=\frac{\mu_0 \times 2I}{2\times 2R}$

$B_2=\frac{\mu_0 I}{2R}$                           (3)

Now as per the question,

$\frac{B_1}{B_2}=\frac{\frac{\mu_0 I}{2R}}{\frac{\mu_0 I}{2R}}$

$\frac{B_1}{B_2}=\frac{1}{1}$

Hence, B₁ divided by B₂ is 1 is to 1 i.e. option (a).