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GATE Electromagnetic question and solution

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In this post, we will see how to approach an electromagnetics question which had appeared in GATE 1995 for 2 marks.

question

Soln: First, let’s understand the question and draw a rough figure based on the question

Ampere s law

As you see, the current direction is towards Z axis. Now the first question is to find out the direction of Magnetic field.

Can the Magnetic field exist in Z direction – No because Magnetic field is perpendicular to the direction of current.

Can the Magnetic field exist in Y direction? Let’s analyse that. Just take two current lines flowing from a plane Y=0, in this case, current is coming out of OUR computer screen, so according to right hand rule, the magnetic field will be in the anti-clockwise direction.

2 current

As you can see the magnetic field at the point due to the 2 current lines is only towards -x direction, thus magnetic field due to infinite current lines contributes only in -x direction and all the y components will be cancelled out.

Now In order to calculate the magnetic field due to the uniform current flowing in the Y=0 plane, we need to consider the small portion of the surface and draw appropriate ‘Amperian loop’ enclosing the current and apply Ampere’s law. In this case the amperian loop will be a rectangular box which is parallel to XY plane and extending an equal distance above and below the surface as shown in the above figure(1).

Applying Ampere’s law

\oint_{C} \vec B. \vec dl = 2Bl=\mu_o I_{enc}=\mu_o Kl where K= Current/metre

So in this case

B=-\mu_o/2 K
H= -K/2 a^x where K=30 mA/m

So the correct Answer is H= -15 a^x mA/m

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