Question

13. Two concentric circular coils A and B have
radii 25 cm and 15 cm and carry currents
10A and 15A respectively. A has 24 turns
and B has 18 turns. The direction of currents
are in opposite order. The magnetic
induction at the common centre of the coil is​

Answer 1

Answer:

B  

1

​  

=  

2 r  

1

​  

 

n  

1

​  

μ  

0

​  

i  

1

​  

 

​  

 

=  

2×25×10  

−2

 

24×μ  

0

​  

×10

​  

 

=4 8 0 μ  

0

​  

 T going into the plane

B  

2

​  

=  

2 r  

2

​  

 

n  

2

​  

μ  

0

​  

i  

2

​  

 

​  

 

=  

2×15×10  

−2

 

18×μ  

0

​  

×15

​  

 

=9 0 0 μ  

0

​  

 T going out of the plane

Bnet=B  

2

​  

−B  

1

​  

 

=(900−4 8 0 ) μ  

0

​  

 

=4 2 0 μ  

0

​  

 T

Explanation:

Answer 2

Given : Radius of A and B is 25 cm and 15 cm respectively.

• Current in A and B is 10 A and 15 A respectively

• Number turns in A and B is 24 and 18 respectively

• The direction of currents are in the opposite order.

To find : The magnetic induction at the common centre of the coil

Solution : Magnetic field due to circular coil A

$B = n1×uo×i1 \: / \: 2r1$

$B = 24×uo×10 \: / \: 2×25×10 {}^{ - 2}$

B1 = 480uo T into the plane

• Magnetic feild due to B

$B = n2×uo×i2 \: / \: 2r2$

$B = 18×uo×15 / 2×15×10 {}^{ - 2}$

B2 = 900uo T out of the plane

• Bnet = B2 - B1

= 900uo - 480uo

Bnet = 420uo T

• Hence, The magnetic induction at the common centre of the coil is 420uo T