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Moving charge and magnetism

Two long parallel wires are at a distance 2d apart. They carry

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Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line $X X^{'}$ is given by :

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Updated on: Aug 16, 2023

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Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line

X X^{'}

is given by :

6 mins ago

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6 mins ago

Text solutionVerified

We know, the magnetic field due to a long current carrying wire is given as

B = \frac{μ _{0} I}{2 π r}

\Rightarrow B \propto \frac{1}{r}

Magnetic field in between the two conductors will be in opposite direction.
Using right hand thumb rule, the magnetic field due to left wire will be in the

\hat{j}

direction while due to the right wire in

(- \hat{j})

direction.
The magnetic field at a distance

x

from the left wire is given as:

B_{in between} = \frac{μ _{0} I}{2 π x} \hat{j} + \frac{μ _{0} I}{2 π ( 2 d - x )} (- \hat{j}) = \frac{μ _{0} I}{2 π} [\frac{1}{x} - \frac{1}{( 2 d - x )}] \hat{j}

x = d, B = 0

x > d, B =

along

- \hat{j}

x < d, B =

along

\hat{j}

On the left side of the left conductor, magnetic field due to the both the conductors will add up and will be along (

- \hat{j})

direction.
On the right side of the right conductor, magnetic field due to the both the conductors will add up and will be along

\hat{j}

direction.
So, option (B) is correct.

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Question Text	Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line $X X^{'}$ is given by :
Updated On	Aug 16, 2023
Topic	Moving Charges and Magnetism
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 7
Upvotes	840
Avg. Video Duration	7 min

Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line $X X^{'}$ is given by :

Text solutionVerified

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Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line $X X^{'}$ is given by :