Question

an electron moves along line AB which lies in the same plane as a circular loop of conducting wire what will be the direction of current induced in loop please answer for my satisfaction this simple question

Answer 1

if the electron moves up in the wire
its magnetic field using right hand thumb rule is inside the loop there fore using again
right hand thumb rule current in loop is anti clock wise but induced is opp to current so induced current is clockwise thi only possible if the magnetic field is given increasing in loop other wise it is clock wise

Answer 2

See diagram.

1) e moves from point A to point B

As the electron travels, it is similar to a current in a wire in the opposite direction.  There is a magnetic field B at point P inside circular loop due to traveling charge.  It is going into the plane of diagram at P.  As the electron nears the magnetic field strength at P increases.  So the flux passing through the area of loop increases.

   The increase in flux causes an EMF to be developed that will oppose increase in flux.  So the induced current will flow anti-clock wise in the loop.

2) e moves from point B to point C.

     Then as e moves away the flux through the loop decreases steadily.  So a current is induced in loop to oppose the decrease.  So the current will change direction and will start flowing in the clock wise direction.

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Detailed answer.

The electron is at 3 positions A, B and C. It is traveling with a speed v in one direction.  Its charge is e.    There is a loop of radius  R  beside the path of e.  The distance between the path and the point P = BP = d.

Biot-Savart's law: