Name: Fleming's Left Hand Rule
Uploaded: 2019-07-19
Duration: 2 min 51 s
Description: In this video, we will look at using Fleming’s left-hand rule to help us remember how current, magnetic fields and direction go together. Get in to know more.

Question

Obtain an expression for magnetic field due to infinitely long straight current carrying conductor by using Amperes law.

Accepted Answer

Consider a point P at a distance r from a straight, infinitely long wire (conductor) carrying a current I in free space as shown in Fig. (a). Because of the axial symmetry about the straight wire, the magnetic induction has the same magnitude B at all points on a circle in a transverse plane and centred on the the wire. We, therefore, choose an Amperian loop a circle of a radius r centred on the wire with its plane perpendicular to the wire, as shown in Fig. (b).

$\vec{B}$ is everywhere tangential to the circular Amperian loop. Therefore, the angle $θ$ between $\vec{B}$ and a length element $\vec{d l}$ is zero at all points of the loop.

$∴ \oint \vec{B} . \vec{d l} = B \oint d l = B (2 π r)$

since $θ = 0$ and B has the same value around the path and $\oint d l$ gives the circumference of the circular loop.

In the figure, the Amperian loop is traced in the anticlockwise sense, so that the current I is taken as positive in accordance with the right hand rule.
By Ampere's law, in free space,

$\oint \vec{B} . \vec{d l} = μ_{0} I$ , where $μ_{0}$ is the permeability of free space.

$∴ B (2 πr) = μ_{0} I B = \frac{μ_{0} I}{2 πr}$

This is the required expression.

Obtain an expression for magnetic field due to infinitely long straight current carrying conductor by using Amperes law.

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