Question

A coil of one loop is made by a wire of length L
and there after a coil of two loops is made by same
wire. The ratio of magnetic field at the centre of
coils respectively :-
(1) 1:4
(2) 1:1
(3) 1: 8
(4) 4:1​

Answer 1

Answer:

Explanation:

Given :  Length of the wire is  L

Let radius of first and second loop be   R  

1

​  

  and  R  

2

​  

 respectively.

According to the question    L=2πR         (first loop)              ..............(1)

Also     L=2×2πR  

2

​  

       (second loop)                         .............(2)

From (1) and (2),        2πR  

1

​  

=2(2πR  

2

​  

)          ⟹  

R  

1

​  

 

R  

2

​  

 

​  

=  

2

1

​  

 

Magnetic field at the center of the coil of radius  R is given by     B=  

2R

μ  

o

​  

nI

​  

 

⟹    

B  

2

​  

 

B  

1

​  

 

​  

=  

n  

2

​  

R  

1

​  

 

n  

1

​  

R  

2

​  

 

​  

=  

2

1

​  

×  

2

1

​  

=  

4

1

​  

                        (∵n  

2

​  

=2,  n  

1

​  

=1)

Thus   B  

1

​  

:B  

2

​  

=1:4