Informative line

### Lenzs Law

Learn Lenz's law definition and examples with explanation, practice to calculate direction of induced current in loop of shape '8' and a Coil while entering and leaving the magnetic field & due to current in another coil.

# Magnetic Flux in Presence of Magnet

• Consider a conducting coil by which galvanometer is connected .
• A bar magnet is placed , as shown in figure.

• Different cases can be applied:

Case 1 :   When bar magnet is stationary

The magnetic flux linked with coil will be constant as the number of field lines passing through coil is constant.

Case 2 :    When bar magnet is moved closer to coil

The magnetic flux linked with coil will increase as the number of field lines passing through coil is increasing.

Case 3 :  When bar magnet is moved away from coil

The magnetic flux linked with coil will decrease as the number of field lines passing through coil is decreasing.

#### In which of the following, are the number of field lines increasing through the loop?

A

B

C

D

×

Magnetic field (B) is inversely proportional to the relative distance between magnet and coil.

Option (A) is correct. Since, the magnet is moving towards loop , the distance between the loop and the magnet decreases . Thus , magnetic field increases which leads to increase in field lines through loop.

Option (B) is incorrect , as the magnet is moving away from the loop, the distance between them is increasing . Thus, magnetic field decreases which leads to decrease in field lines through loop.

Option (C) is incorrect because the magnet and the loop, both are moving with same speed. Thus, there is no change in distance and magnetic field , which leads to the constant field lines through loop.

Option (D) is incorrect because both the magnet and the loop are moving away from each other . Thus the distance between them is increasing. Hence, the magnetic field is decreasing which leads to decrease in field lines through loop.

### In which of the following, are the number of field lines increasing through the loop?

A
B
C
D

Option A is Correct

# Direction of Induced Current in a Coil while Entering and Leaving the Magnetic Field

## Lenz's Law

• Lenz's Law states that the change in magnetic flux, induce the current in a closed conducting loop whose direction is such that the induced magnetic field opposes the change  in the flux.
• Consider a loop moving with velocity $$v$$ such that it enters in the region of magnetic field.

### Direction of Induced Current in the Coil while Entering

• While entering, the flux is changing as the number of crosses (which represents magnetic field) enclosed by the loop are increasing ,as shown in figure.

• Now, due to this, a current is induced in the loop.
• The direction of induced current will be such that the magnetic field created by it will be in opposite direction to the present magnetic field.
• Since, the number of crosses (amount of magnetic field) increases , thus the  induced current will be such that it opposes the present magnetic field .
• Hence, the direction of induced current will be anticlockwise , So that it opposes the change of flux and the field created by the current will be perpendicularly out of page while the present field is perpendicularly into the page.

### Direction of Induced Current in the Coil while Leaving

• When loop leaves the magnetic field , then the number of crosses enclosed by the loop decreases.
• In this situation, the direction  of current will be such that the induced magnetic field maintains the original flux through the loop.
• Thus, the direction of induced current will be clockwise and the field created by it will be perpendicularly into the page which is same as the direction of present field.

Note: We can assume the direction of induced current in any direction, as it comes with its sign while calculating.

#### A loop leaves a magnetic field region with uniform velocity $$v$$ in 4 sec. What should be the direction of induced current from the time it starts to leave till it completely leaves the magnetic field?

A Clockwise

B Anticlockwise

C No current

D None of these

×

When loop leaves the magnetic field , then the number of crosses enclosed by the loop decreases.

In this situation, the direction  of current will be such that the induced magnetic field maintains the original flux through the loop.

Thus, the direction of induced current will be clockwise.

Hence , option (A) is correct.

### A loop leaves a magnetic field region with uniform velocity $$v$$ in 4 sec. What should be the direction of induced current from the time it starts to leave till it completely leaves the magnetic field?

A

Clockwise

.

B

Anticlockwise

C

No current

D

None of these

Option A is Correct

# Direction of Induced Current in Loop of Shape '8'

• Consider a loop of shape as shown in figure, which is placed in a magnetic field.
• The wire of loop has $$\lambda$$ resistance per unit length.
• The radius of upper circle of loop is $$r_U$$  and the radius of lower circle of loop is $$r_L$$.
• Here, $$r_L$$ is greater than $$r_U$$.

## Direction of Induced Current

• Consider a loop, as shown in figure, which is present in an increasing magnetic field.
• The area of loop $$II$$ is more.Thus, more flux is passing through it.
• Hence, the direction of current in loop  $$II$$  will be anti-clockwise.

• To determine the direction of induced current in loop $$I$$, consider both loops are present separately in same increasing magnetic field.
• Now, the direction of induced current in both loops will be anticlockwise. But, the magnitude of current in loop $$II$$ will be more as compared to the magnitude of current in loop $$I$$.
• So, net current in bigger loop will be anticlockwise and hence, in upper loop it will be clockwise.

#### What will be the direction of net induced current in loop $$I$$, if the magnetic field present, is increasing?

A Clockwise

B Anticlockwise

C No Current

D None of these

×

Due to increasing magnetic field, the direction of induced current in loop $$II$$ is anticlockwise.

The net current will flow in anticlockwise direction in lower loop because area is bigger. Hence, it will be in clockwise direction in upper loop.

Hence, option (A) is correct.

### What will be the direction of net induced current in loop $$I$$, if the magnetic field present, is increasing?

A

Clockwise

.

B

Anticlockwise

C

No Current

D

None of these

Option A is Correct

# Direction of Induced Current Due to Moving Rod

• Consider a rod which is placed over two clamped rails.
• The rod can only move in right and left side.
• This system is placed in uniform magnetic field, as shown in figure.

### Direction of induced current, when rod moves towards left side with some velocity

• When the rod moves towards left side, the area enclosed by magnetic field decreases.Thus, the number of crosses decrease.

• As a result, the flux decreases.
• Since, the flux decreases, thus $$\dfrac{d\phi}{dt}$$ will be negative.
• According, to Lenz's law, in order to maintain the changing flux, the direction of current will be clockwise.

### Direction of induced current, when rod moves towards right side with some velocity

• When the rod moves towards right side, the area enclosed by magnetic field increases. Hence, the number of crosses increase.

• As a result, the flux increases.
• Since, the flux increases, thus $$\dfrac{d\phi}{dt}$$ will be positive.
• According  to Lenz's law, in order to maintain the changing flux, the direction of current will be anticlockwise.

#### If the rod is moving with velocity $$v = 2\,m/s$$, then what will be the direction of induced current in the system shown in figure?

A Anticlockwise

B Clockwise

C No current

D None of these

×

When the rod moves towards right side, the area enclosed by magnetic field increases. Hence, the number of crosses increase.

As a result, the flux increases.

Since, the flux increases, thus $$\dfrac{d\phi}{dt}$$ will be positive.

According  to Lenz's law, in order to maintain the changing flux, the direction of current will be anticlockwise.

Hence, option (A) is correct.

### If the rod is moving with velocity $$v = 2\,m/s$$, then what will be the direction of induced current in the system shown in figure?

A

Anticlockwise

.

B

Clockwise

C

No current

D

None of these

Option A is Correct

# Lenz's Law

Lenz's Law states that the change in magnetic flux, induce the current in a closed conducting loop whose direction is such that the induced magnetic field opposes the change  in the flux.

• Consider a loop which is at rest and placed in a uniform magnetic field.

## Direction of induced current in the coil when magnetic field is increased

• When magnetic field is increased then the number of crosses (which represents magnetic field ) increases.
• Now, due to this, a current is induced in the loop.
• Since, the number of crosses (amount of magnetic field) increases, thus the  induced current will be such that it opposes the present magnetic field.
• Hence, the direction of induced current will be anticlockwise, so that, it opposes the change of flux, and the field created by the current will be perpendicularly out of page while the present field is perpendicularly into the page.

## Direction of induced current in the coil when magnetic field is decreased

• When magnetic field is decreased then the number of crosses (which represents magnetic field ) decreases.
• Now, due to this, a current is induced in the loop.
• In this situation, the direction of current will be such that the induced magnetic field maintains the original flux through the loop.
• Thus, the direction of induced current will be clockwise and the field created by it will be perpendicularly into the page which is same as the direction of present field.

#### What should be the direction of current, when north pole of a bar magnet is moved closer to conducting loop which is kept at rest?

A Clockwise

B Anticlockwise

C No Current

D None of these

×

According to Lenz's law, the change in magnetic flux induce the current in a closed conducting loop whose direction is such that the induced magnetic field opposes the change in the flux.

Hence, direction of current must  be anticlockwise as seen from right side of loop.

### What should be the direction of current, when north pole of a bar magnet is moved closer to conducting loop which is kept at rest?

A

Clockwise

.

B

Anticlockwise

C

No Current

D

None of these

Option B is Correct

# Direction of Induced Current in a Coil Due to Current in Another Coil

• Consider two loops (A and B ) which are placed co- axially, as shown in figure.
• In loop A,current is flowing in anticlockwise direction with constant magnitude,as seen from right side of the loop.
• The induced current in loop B is zero.

## Induced current in loop B, when current in loop A is increased

• As the magnitude of current is increased, more number of lines are passing through loop B to oppose the change in magnetic field.
• Thus current should be in opposite direction.
• The current should be in clockwise direction.

## Induced current in loop B, when current in loop A is decreased

• As the magnitude  of current is decreased in the loop A, the number of field lines passing through loop B will decrease.
• Thus, to maintain the enclosed magnetic field, the direction of induced current must be same.
• Hence, the current should be in anticlockwise direction, as seen from right side of loop.

#### What will be the direction of induced current in loop B, if current in loop A is decreased?

A Anticlockwise

B Clockwise

C No Current

D None of these

×

As the magnitude  of current is decreased in the loop A, the number of field lines passing through loop B will decrease.

Current should be in anticlockwise direction as seen from right side of loop.

Hence, option (A) is Correct.

### What will be the direction of induced current in loop B, if current in loop A is decreased?

A

Anticlockwise

.

B

Clockwise

C

No Current

D

None of these

Option A is Correct

# Direction of Force Created by Induced Current

• Consider a coil. A bar magnet is bring closer to it, as shown in figure.

• As a result, the number of field lines passing through the coil increases.
• Due to increase in field lines i.e. increase in number of dots, current is induced in coil in anticlockwise direction as seen from the right side of loop.
• The induced current produces its magnetic field in the opposite direction of the magnetic field of bar magnet.
• By above observations, it can be concluded that the coil behaves like a bar magnet with opposite poles.

Thus, the bar magnet will experience a repulsive force towards itself.

### Case I

• As the magnet moves towards the coil, the external magnetic flux through the coil increases. To oppose this change in flux, an induced current is produced in coil.
• The induced current produces its own magnetic field in opposite direction to the magnetic field of magnet. So as to conserve the energy generated in coil, some work is to be done to displace the magnet towards the coil.
• The left side of the coil will act as south pole and right side of coil will act as north pole. And hence, magnet will experience a repulsive force.

### Case II

• As the magnet moves away from coil, the external magnetic flux through the coil decreases. To oppose this change in flux, an induced current is produced in coil.
• The induced current produces its own magnetic field in the direction of magnetic field of magnet. So as to conserve the energy generated in coil, some work is to be done to displace the magnet away from coil.
• The, m left side of coil will act as north pole and right side of coil will act as south pole. And henceagnet will experience an attractive force.

#### If the magnet is moving with velocity, $$v = 3 (-\hat i)$$ towards coil, then what will be the direction of force experienced by the magnet?

A $$+\hat j$$

B $$-\hat j$$

C $$+\hat i$$

D $$+\hat k$$

×

As magnet is moving closer to coil, the magnetic field increases and induce current in coil in anticlockwise direction.

The induced current produces its magnetic field in the opposite direction of the magnetic field of bar magnet.

Thus, the direction of force experienced by bar magnet will be in $$(+\hat i)$$ direction.

Hence, option (C) is correct.

### If the magnet is moving with velocity, $$v = 3 (-\hat i)$$ towards coil, then what will be the direction of force experienced by the magnet?

A

$$+\hat j$$

.

B

$$-\hat j$$

C

$$+\hat i$$

D

$$+\hat k$$

Option C is Correct

#### If direction of force experienced by magnet is $$(+\hat j)$$, then which option is correct?

A

B

C

D

×

Option (A) is incorrect because the relative velocity of magnet and coil is zero . Thus , there is no change in flux through coil . Hence , no force is experienced by magnet.

Option  (B) is incorrect because the magnet is moving away from coil . Thus ,the magnetic flux decreases through  the coil . Hence, the force experienced by  magnet is in $$(- \hat i)$$  direction.

Option (C) is incorrect because the relative velocity of magnet and coil is zero . Thus , there is no change in flux through coil . Hence , no force is experienced by magnet.

Option (D) is correct because the magnet is moving towards the coil. Thus , the magnetic flux increases through the coil. Hence, the force experienced by  magnet is in $$(+\hat j)$$  direction .

### If direction of force experienced by magnet is $$(+\hat j)$$, then which option is correct?

A
B
C
D

Option D is Correct