Question

Show that there is no magnetic field at the centre of circular loop of radius r, irrespective of value of angle theta
​

Answer 1

Explanation:

Correct option is

C

inward as long as θ is less than π

Magnetic field at O due to curved portion: B

curved

=

2R

μ

0

i

×

2π

θ

is out of the plane of the paper

Magnetic field at O due to the straight wire: B

wire

=

4πd

μ

0

i

×2sin(

2

θ

) where d=Rcos

2

θ

⇒B

wire

=

4πRcos

2

θ

μ

0

i

2sin(

2

θ

)=

2πR

μ

0

i

tan

2

θ

into the plane of the paper.

The net magnetic field B

net

=B

wire

−B

curved

=

2πR

μ

0

i

(tan

2

θ

−

2

θ

)

For θ>π B

net

, is negative ie. it is out of the plane of the paper.