One end of a bar is in contact with a circular rail and the other end is pivoted

Question

One end of a bar is in contact with a circular rail and the other end is pivoted at P. A steady, uniform, magnetic field B is present. The bar rotates about P.

In the following situations and figures, is the induced current in the resistor from a to b or from b to a? One end of a bar is in contact with a circular rail and the other end is pivoted at P. A steady, uniform, magnetic field B is present. The bar rotates about P. Two parallel wires carry a current I in opposite directions. A rectangular loop is midway between the wires. The current I is decreasing. A bar is in contact with a pair of parallel rails. A steady, uniform, magnetic field, perpendicular to the plane of the rails, is present. The bar is in motion with velocity v.

Explanation / Answer

Area of Loop is decreasing
flux=B.A
Area, A is decreasing
=> Flux in it is decreasing since
=> current induced will oppose the change---> Lenz law
i.e it will increse the flux across loop
i; Current will be from a to b

b) Flux due to current carrying wire is decreasing
since B is decreaseing as B=uI/(2*pie*R)
Morever B is going inside of paper
Hence
current induced will oppose the change---> Lenz law
i.e it will increse the flux across loop
i; Current will be from a to b

c)
Area of Loop is decreasing
flux=B.A
Area, A is decreasing
=> Flux in it is decreasing since
=> current induced will oppose the change---> Lenz law
i.e it will increse the flux across loop
i.e B due to current should be coming out of paper
=> Current would be from b to a

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