Question

The figure shows a stationary conducting loop adjacent to a vertical current carrying wire. For which of the following conditions will a clockwise induced current circulate in the stationary loop? Current-carrying wire Stationary conducting loop Clockwise induced current The current in the vertical wire flows downward and its value is decreasing. The current in the vertical wire flows downward and its value is constant. The current in the vertical wire flows upward and its value is increasing The current in the vertical wire flows upward and its value is decreasing The current in the vertical wire flows upward and its value is constant

Answer 1

Let's assume wire is along z-axis and conducting loop is in x-z plane as shown in figure.

S 2 2 ()

Given induced current in the loop is in clockwise direction.

Therefore according to right hand rule curl your right hand fingers along the direction of current then the direction of the thumb is direction of magnetic field.

Therefore we can see the direction of magnetic field due to induced current in the conduction loop is along +y-axis.

We know in a loop a current can induced only due to time varying magnetic flux. Therefore flux passes through the loop must vary with time.

Now we know magnetic field due to current I carrying conductor at a fixed distance r is given by

$B=\frac{\mu_0I}{2\pi r}$

Therefore if current I is constant B will be constant therefore magnetic flux passes through the loop will be constant if I 8s not varying with time. Therefore option (2) and (5) are ruled out.

Now according to lenz's law the direction of magnetic field due to induced current always directed in such a way so that it can oppose the change in magnetic flux through the loop.

Option (1) as the current flowing downward therefore according to right hand rule direct you right hand thumb along the direction of current then curl your fingers. Direction of curling is direction of magnetic field. Therefore we can see direction of magnetic flux through the loop is along negative y-axis. Since current is decreasing with time therefore magnetic flux through the loop decreasing with the time. Therefore to oppose this change the magnetic field due to induced current must be directed along negative y-axis therefore this option can't be correct.

Option (3) again as explained above we can see this time magnetic flux passes through the loop directed along +y-axis by this time current is increasing with time therefore magnetic field due to the induced current must be directed along negative y-axis to oppose this change. Therefore this option is ruled out.

Option (4) as explained above the magnetic field due to the current carrying wire is directed along +y-axis and since current is decreasing with time therefore magnetic flux through the loop is decreasing with time and to oppose this change the magnetic field due to the induced loop must be directed along +y-axis. It's the direction of the given case.

Therefore option (4) is correct answer.