Question

Deduce expression for magnetic field due to a current carrying thick wire at following points 1. Outside the wire 2. At the surface of the wire 3. Inside the wire 4. At the center.of the wire.

Answer 1

Answer:

According to Biot-Savart Law, magnetic field due to a current carrying element dl is:

dB

=

4πr

3

μ

o

I

(

dl

×

r

)

The magnetic field due to a current carrying circular loop is shown in the figure. Vertical components of the magnetic field cancel out by the diametrically opposite end on the wire.

Horizontal component due to an element dl is given by:

dB=

4πr

2

μ

o

I

sinθdl

dB=

4πr

3

μ

o

IR

dl

∫dB=

4πr

3

μ

o

IR

∫dl

B=

4π(R

2

+x

2

)

3/2

μ

o

IR

2πR

B=

2(R

2

+x

2

)

3/2

μ

o

IR

2