What will this loop oppose?

A loop A B C D ABCD is placed in the plane of an infinite current-carrying wire, as shown in the diagram.

The current in the wire varies as i = i 0 e 2 t i=i_0 e^{-2t} . What will be the direction of induced current in the loop?

Clockwise Anticlockwise No current will induce in the loop

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1 solution

Rohit Gupta
Jan 17, 2017

The direction of the magnetic field produced by the current carrying wire can be found out using the right hand rule. It will come out to be into the plane of the loop. Therefore, due to the current in the wire, there will be a magnetic flux (going into the plane of the loop) linked with the loop. As the current changes with time, this magnetic flux crossing the loop also changes.

According to the Lenz's law , an emf is induced in the loop in such a way that to oppose its own cause.

According to the equation of the current, the current is decreasing and hence the magnetic flux through the loop is decreasing. The induced emf will oppose this decrease in the magnetic flux and hence the induced emf/current will be in the clockwise direction. \boxed{\textbf{the induced emf/current will be in the clockwise direction.}}

Please tell me where I messed up my logic. The magnetic flux is into the plane and decreasing. Therefore the induced magnetic field is also into the plane. Using the right hand rule (thumb: mangetic field and fingers curl in the direction of current) you get the current going clockwise.

John Crocker - 4 years, 4 months ago

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It is my bad. I have corrected the options. Clockwise is correct.

Rohit Gupta - 4 years, 4 months ago

Thanks. I see that this problem has been edited. Those who previously answered "Clockwise" has been marked correct.

In future, if you spot any errors with a problem, you can “report” it by selecting "report problem" in the menu. This will notify the problem creator (and eventually staff) who can fix the issues.

Brilliant Mathematics Staff - 4 years, 4 months ago

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