Question

wire of radius 0.5 cm carries a current of 100 A, which is uniformly distributed over its cross-section. Find the magnetic field
(i) at 0.1 cm from the axis of the wire,
(ii) at the surface of the wire and
(iii) at a point outside. the wire 0.2 cm from the surface of the wire.

Answer 1

Given: wire of radius 0.5 cm carries a current of 100 A, which is uniformly distributed over its cross-section

To find: Find the magnetic field

(i) at 0.1 cm from the axis of the wire,

(ii) at the surface of the wire and

(iii) at a point outside. the wire 0.2 cm from the surface of the wire.

Solution: a) since we need to find a magnetic field at a point which is at a distance of 0.1 cm from the axis, that means that point is inside the wire.

So magnetic field due to current carrying wire at. a point which is inside the wire will be

Bins= μ0/4π × ( 2Ir/R^2)

where Bins is the magnetic field inside the wire, I is current in the wire, r is a distance of the point from the axis, R is the radius of the wire

putting the values we will get a magnetic field

Bins= 10^-7 ×( 2×100× 0.1× 100^-2)/ ( 0.5×10^-2)^2

Bins= 2/2500

Bins = 8× 10^-4 T

the magnetic field at 0.1 cm from the axis of the wire is 8× 10^-4 T.

b) Bsurface = μ0/4π × ( 2I/R)

Bsurface = 10^-7 × ( 2×100/5× 10^-3)

Bsurface = 4×10^-3 T

the magnetic field at the surface of the wire is 4×10^-3T.

c) magnetic field at a point 0.2 distance from the surface that means its distance from the axis will be 0.5+0.2 = 0.7cm

Boutside = μ0/4π × ( 2I/r)

Boutside = 10^-7 ( 2× 100/ 7×10^-3)

Boutside = 0.286 ×10^-2T

the magnetic field at a point outside the wire will be 2.8×10^-3T.