Question

A cell is connected between two points of a uniformly thick
circular conductor and i₁ and i₂ are the currents flowing in
two parts of the circular conductor of radius a. The magnetic
field at the centre of the loop will be
(a) zero (b) μ₀/4π (I₁ - I₂ )
(c) μ₀/2a (I₁ + I₂ )
(d) μ₀/a (I₁ + I₂ )

Answer 1

answer : zero

explanation: Let l

1

,l

2

be the length of the two parts PRQ and PSQ of the conductor and ρ be the resistance per unit length of the conductor. The resistance of the portion PRQ will be R

1

=l

1

ρ

The resistance of the portion PSQ will be R

2

=l

2

ρ

Pot. diff. across P and Q =I

1

R

1

=I

2

R

2

or I

1

l

1

ρ=I

2

l

2

ρ or I

1

l

1

=I

2

l

2

....... (1)

Magnetic field induction at the centre O due to currents through circular conductors PRQ and PSQ will be

=B

1

−B

2

=

4π

μ

0

r

2

I

1

l

1

sin90

o

−

4π

μ

0

r

2

I

2

l

2

sin90

o

=0