Question

Two similar coils of radius R are lying concentrically with
their planes at right angles to each other. The currents
flowing in them are I and 2 I, respectively. The resultant
magnetic field induction at the centre will be
(a) √5μ₀I/2R
(b) 3μ₀I/2R
(c) μ₀I/2R
(d) μ₀I/R

Answer 1

Answer:

a)

Explanation:

Magnetic field at center due to first coil is B

1

=

2R

μ

0

I

Magnetic field at center due to second coil perpendicular to the first is B

2

=

2R

μ

0

(2I)

Hence net magnetic field at the center=

B

1

2

+B

2

2

=

2R

5

μ

0

I

Answer 2

Explanation:

Magnetic field at center due to first coil is B

1

=

2R

μ

0

I

Magnetic field at center due to second coil perpendicular to the first is B

2

=

2R

μ

0

(2I)

Hence net magnetic field at the center=

B

1

2

+B

2

2

=

2R

5

μ

0

I