Q. 65.0( 3 Votes )

A long, straight wire of radius r carries a current i and is placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross section.

(a) At what points will the resultant magnetic field have maximum magnitude?

(b) What will be the minimum magnitude of the resultant magnetic field?


Answer :


Given:
Radius of the wire : r
Current through the wire : i
Uniform magnetic field pointing upward : B

Formula used:
Magnetic field due to a current carrying wire is

Magnitude of magnetic field due to wire,


Where, μ0 is the permeability of free space and μ0= 4π × 10-7 T mA-1.


r is the radius of the wire.
(a)
Maximum net magnetic field would be above the wire at P.
Considering direction of the current as shown in the diagram, right hand rule will give us direction of the magnetic field due to wire.
thus,
Bnet = B+Bw
Bnet = B +
(b)
Similarly, the field at Q would be in opposite direction to the P.
Minimum magnitude of the magnetic field will be a Q
Bnet = B-Bw
Bnet = B -
Hence, magnitude of magnetic field will be maximum at points above at wire and minimum at points below the wire only if the direction of the current is as shown in the figure.


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