The Magnetic Field at the Centre of a Circular Arc Inclined at π/2 is

A

µ 8 0 R i µ 4 0 R i µ 8 0 R i µ 3 0 R i By Team Aakash Byju's | 12th December 2022

Detailed Explanation

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Given that, the arc subtends an angle π/2 at the centre. Hence, it is a right angle.

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To find the magnetic field at the centre of the arc as shown in the image, we need to apply Biot Savart's Law. The magnetic field due to a current-carrying arc is

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To find the net charge, we take the integration of this magnetic field,

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Since

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A

D

B

C

The Magnetic Field at the Centre of a Circular Arc Inclined at π/2 is

Detailed Explanation

The correct answer is option A.

µ

8

R

i

Given that, the arc subtends an angle π/2 at the centre. Hence, it is a right angle.

C

Let us visualise the given situation - the centre of the circle is C and the radius is R.

>

π

2

R

R

To find the magnetic field at the centre of the arc as shown in the image, we need to apply Biot Savart's Law. The magnetic field due to a current-carrying arc is

=

π

C

π

π

2

>

R

R

To find the net charge, we take the integration of this magnetic field,

dB =∫

∫

idl

=>

B =

i

∫

dl

R

R

C

µ

4

π

µ

4

π

>

π

2

R

R

Since

we get,

∫

dl

= Rθ

B =

i

Rθ

Given,

θ

=

π

2

=>

B =

i

R

π

2

=

(Hence the answer.)

C

R

µ

4

π

µ

4