Question

Problem 7: For each situation shown below, indicate • the direction of the area vector you have chosen (direction of positive flux) the sign of the flux using that area vector • whether the flux is increasing or decreasing the direction of the induced magnetic field • the direction of the induced current .

Answer 1

Before Answer the questions, note some points on the basis I will explain :

1) Area vector is perpendicular to the plane of loop. [here I will consider the normal outward of plane of loop to be positive]

2) If angle between area vector and magnetic field is between 0 to 90 degree, then magnetic flux is positve.

3) If angle between area vector and magnetic field is between 90 to 180 degree, then magnetic flux is negative.

4) If any of area, magnetic field or magnitude of cosine of the angle between area vector and magnetic field increases then flux increases. Also, we need to check overall sometimes for multiple variations.

5) If magnetic field is observed inward to the loop and magnetic flux increases, then current induced is counter clockwise, induced magnetic field is outward.

6) If magnetic field is observed inward to the loop and magnetic flux decreases, then current induced is clockwise, induced magnetic field is inward.

7) If magnetic field is observed outward to the loop and magnetic flux increases, then current induced is clockwise, induced magnetic field is inward.

8) If magnetic field is observed outward to the loop and magnetic flux decreases, then current induced is counter clockwise, induced magnetic field is outward.

Now,

a) Area vector positve. [refer point 1]

As due to the indicated current, the direction of magnetic field is inward using right hand thumb rule. The angle between area vector and magnetic field is 180 degree, so magnetic flux is negative. [refere point 3]

as the current is increasing, flux in increasing. [refer point 4]

induced magnetic field is outward. [refer point 5]

  current induced is counter clockwise. [refer point 5]

Force on nearby side is greater and when current are in same direction, force is attractive. When direction of current induced is counter clockwise, current induced on the nearby side is opposite to given current, so effectively, the force is repulsive.

b) Area vector positve. [refer point 1]

As due to the indicated current, the direction of magnetic field is inward using right hand thumb rule. The angle between area vector and magnetic field is 180 degree, so magnetic flux is negative. [refere point 3]

as nothing is variable with time, flux is constant.

when flux is constant, there is no induced current and no induced magnetic field and no force experienced.

c) Area vector positve. [refer point 1]

The direction of magnetic field is inward, The angle between area vector and magnetic field is 180 degree, so magnetic flux is negative. [refere point 3].

Area is decreasing, so flux is decreasing. [opposite of point 4]

current induced is clockwise, induced magnetic field is inward. [refer point 6]

Net force on a current carrying loop due to uniform magnetic field is zero.

d) From the magnet side, area vector is taken positive.

Magnetic field emerging from North pole of magnet, so it will enter the loop,angle between area vector and magnetic field is 180 degree, so, magnetic flux is negative. [refer point 3]

as the magnet is moving away , magnetic field decreses, flux is decreasing.

current induced is clockwise, induced magnetic field is inward. [refer point 6]

The force on the loop is attractive in nature.

e) From right side when viewed , area vector is taken positive.

Magnetic field due to solenoid is from left to right,and thriugh loop, it is outside, angle between area vector and magnetic field is 0 degree, so flux is positive.

As current is decreasing, flux is decreasing.

current induced is counter clockwise, induced magnetic field is outward. [refer point 8]

There is no magnetic field outside the solenoid, so the loop does not experience any force.