Question

A battery is connected between two points
A and B on the circumference of a uniform
conducting ring of radius r and resistance R.
One of the arcs AB of the ring subtends an
angle 0 at the centre. The value of the
magnetic induction at the centre due to the
current in the ring is​

Answer 1

Answer:

Magnetic field at the centre due to current ABC arc is

B

1

=

4π

μ

0

r

2πI

1

2π

θ

(Directed upwards)

Magnetic field at the centre due to current in ADC arc is

B

2

=

4π

μ

0

r

2πI

2

2π

(2π−θ)

(Directed downwards)

Therefore net magnetic field at the centre

B=

4π

μ

0

r

2πI

1

2π

θ

−

r

2πI

2

2π

(2π−θ)

Also, I

1

=

R

1

V

=

ρl

1

/A

V

=

ρrθ

VA

and

I

2

=

R

2

V

=

ρl

2

/A

E

=

ρr(2π−θ)

VA

∴B=

4π

μ

0

[

ρrθ

VA

×

r

θ

−

ρr(2r−θ)

VA

×

r

(2π−θ)

]=0