Question

What is the current in a long wire if the magnetic field strength 1.6 cm from the wire's axis is 53 µT?

Answer 1

Concepts and reason

The concept required to solve the given question is Ampere’s circuital law.

First, consider the expression for Ampere’s circuital law.

Later rearrange the equation to obtain the expression for current in a long wire, by substituting the values of permeability of free space, length of the wire, and magnetic field.

Finally, calculate the current in the long wire.

Fundamentals

Ampere’s Circuital law:

Consider a long thin wire, carrying a current. The orientation of the wire is in such a way that the current is flowing through the z – axis. Then, the law states that “the line integral of magnetic field around some closed loop is equal to times the algebraic sum of currents which pass through the loop.

Here, B is the magnetic field, is the length of the small straight line element of the loop, is the permeability of free space, and I is the algebraic sum of the currents passing through the loop.

Use Ampere’s Circuital law.

The line integral of magnetic field through a closed loop is,

The above expression can be rewritten as,

$B= $

Here, B is the magnetic field, is the permeability of free space, and is the length of the wire.

Rearrange the above equation for I.

……(1)

Current passing through the wire:

The expression for the current flows in the wire from equation (1) is,

Substitute 3.14 for , for r, for B, and for in the equation to calculate I.

Ans:

The current in the long wire is .