- A d.c. A motor works on the principle that a current-carrying conductor placed normally in a magnetic field experiences a force, producing rotational motion.
- The split ring commutator reverses the direction of current in the coil after every half rotation, so that the coil continues to rotate in the same direction.
- The armature coil experiences an anticlockwise couple due to equal and opposite forces on its arms, causing continuous rotation of the coil.
- In a d.c. Motor, electrical energy supplied by the battery is converted into mechanical energy.
Definitions [9]
Definition: Right Hand Thumb Rule
If a current-carrying straight conductor is held in the right hand such that the thumb points in the direction of the electric current, then the fingers curled around the conductor show the direction of the magnetic field.
This is called the Right-Hand Thumb Rule.
OR
If you hold a current-carrying conductor in your right hand with the thumb pointing in the direction of the current, then the curled fingers show the direction of the magnetic field (lines of force) around the conductor.
Definition: Solenoid
If a conducting wire is wound in form of a cylindrical coil whose diameter is less in comparison to its length, the coil is called a solenoid.
OR
A coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder is called a solenoid.
OR
When a copper wire with a resistive coating is wound in a chain of loops (like a spring), it is called solenoid.
Definition: Electromagnet
An electromagnet is a temporary strong magnet made by passing current in a coil wound around a piece of soft iron. It is an artificial magnet.
Definition: Simple D.C. Motor
An electric motor is a device which converts the electrical energy into the mechanical energy.
Definition: Electromagnetic Induction
Whenever there is a change in the number of magnetic field lines linked with a conductor, an electromotive force (e.mf) is developed between the ends of the conductor which lasts as long as there is a change in the number of magnetic field lines through the conductor. This phenomenon is called the electromagnetic induction.
and
Faraday's Definition:
Electromagnetic induction is the phenomenon in which an e.m.f is induced in the coil if there is a change in the magnetic flux linked with the coil.
Define the right-hand thumb rule.
If the current-carrying conductor is held in the right hand such that the thumb points in the direction of the current, then the direction of the curl of the fingers will give the direction of the magnetic field.
Definition: Faraday's Law of Induction
Whenever the number of magnetic lines of force (magnetic flux) passing through a coil changes, an electric current is induced in the coil. This current is called the induced current.
Definition: A.C. Generator
An a.c. generator is a device which converts the mechanical energy into the electrical energy using the principle of electromagnetic induction.
Define a Transformer.
The transformer is a device used for converting low voltage into high voltage and high voltage into low voltage. It works on the principle of electromagnetic induction.
Formulae [1]
Formula: Magnetic Force on a Straight Current-Carrying Conductor
\[\vec{F}=I\vec{l}\times\vec{B}\]
Theorems and Laws [3]
State Lenz’s Law.
It is stated that the direction of induced e.m.f. is always in such a direction that it opposes the change in magnetic flux.
e = `(d phi)/(dt)`
Consider a rectangular metal coil PQRS. Let ‘L’ be the length of the coil. It is placed in a partly magnetic field ‘B’. The direction of the magnetic field is perpendicular to the paper and into the paper. The ‘x’ part of the coil is in magnetic field at instant t. If the coil is moved towards the right with a velocity v = dx/dt with the help of an external agent, such as a hand. The magnetic flux through the coil is:
Φ = BA = BLx
∴ Φ = BLx ...(1)
There is relative motion of a current through the coil. Let ‘i’ be current through the coil.
Three forces act on the coil.
F1 on conductor PL ∴ F1 = Bi x, vertically upward.
F2 on conductor MS ∴ F2 = Bi x, vertically downward.
F3 on conductor SP ∴ F3 = Bi L towards left.
F1 & F2 are equal and opposite and also on the same lines. They will cancel each other; F3 is a resultant force. The external agent has to do work against this force.
∴ F3 = −Bi l ...(−ve sign indicates that force is opposite to dx.)
If dx is the displacement in time dt, then the work done (dw) = F3 dx.
∴ dw = − BiL dx
This power is an electrical energy ‘ei’ where ‘e’ is an induced e.m.f.
∴ ei = `-(B_i ldx)/(dt)`
∴ e = `-(BLdx)/(dt)`
∴ e = −BLv
∴ e = `-d/dt (BLx)`
∴ e = `(-d phi)/(dt)` ...[from eq (1)]
Lenz’s Law states that the direction of the induced electromotive force (EMF) and the resulting current in a conductor is always such that it opposes the change in magnetic flux that caused it.
Mathematically, Lenz’s Law is expressed as:
ε = `(-d phi_B)/dt`
Where,
ε = Induced EMF
ΦB = Magnetic flux
The negative sign indicates opposition to the change in flux.
Law: Faraday's First Law or Neumann’s law
Statement:
When the magnetic flux through a circuit is changing, an induced electromotive force (emf) is set up in the circuit whose magnitude is equal to the negative rate of change of magnetic flux. This is also known as Neumann’s Law.
Mathematical Expression:
If ΔΦB is the change in magnetic flux in a time interval Δt, then the induced emf e is given by:
e = \[-\frac{\Delta\Phi_B}{\Delta t}\]
In the limiting case as Δt → 0:
e = \[-\frac{d\Phi_{B}}{dt}\]
- If dΦB is in weber (Wb) and dtdtdt in seconds (s), then the emf eee will be in volts (V).
- This equation represents an independent experimental law, which cannot be derived from other experimental laws.
For a tightly-wound coil of N turns, the induced emf becomes:
e = \[-N\frac{d\Phi_B}{dt}\] or e = \[-\frac{d(N\Phi_B)}{dt}\]
Here, NΦB is called the ‘number of magnetic flux linkages’ in the coil, and its unit is weber-turns.
Explanation:
Consider a magnet and a coil:
- When the north pole of a magnet is near a coil, a certain number of magnetic flux lines pass through the coil.
- If either the coil or the magnet is moved, the number of magnetic flux lines (i.e., the magnetic flux) through the coil changes.
Cases:
- Magnet moved away from the coil → Decrease in magnetic flux through the coil.
- Magnet brought closer to the coil → Increase in magnetic flux through the coil.
In both cases, an emf is induced in the coil during the motion of the magnet.
- Faster motion → Greater rate of change of flux → Higher induced emf.
- If both the magnet and coil are stationary, or both are moving in the same direction with the same velocity, there is no change in flux → No induced emf.
Special Case:
- If the coil is an open circuit (i.e., infinite resistance), emf is still induced, but no current flows.
- This shows that it is the change in magnetic flux that induces emf, not current.
Conclusion:
Neumann’s Law establishes that a changing magnetic flux through a circuit induces an emf, and the induced emf is proportional to the rate of change of flux, with a negative sign indicating the direction (as per Lenz’s law).
Limitations:
- The law applies to changing magnetic flux; it does not induce emf if the magnetic flux remains constant.
- No emf is induced if the coil and magnet move together at the same velocity or remain stationary.
- In open circuits, emf is induced, but no current is generated.
Law: Faraday's Second Law or Lenz's Law
Statement:
The direction of the induced emf, or the induced current, in any circuit is such as to oppose the cause that produces it. This law is known as Lenz’s Law.
Explanation / Proof:
- When the north pole of a magnet is moved towards the coil, an induced current flows in the coil in such a direction that the near (left) face of the coil behaves like a north pole.
- Due to the repulsion between the like poles, the motion of the magnet towards the coil is opposed.
- When the north pole of the magnet is moved away from the coil, the induced current flows in such a direction that the near face of the coil becomes a south pole.
- The attraction between opposite poles then opposes the motion of the magnet away from the coil.
In both cases, the induced current opposes the magnet's motion, which is the cause of the current. Therefore, work has to be done to move the magnet, and this mechanical work appears as electrical energy in the coil.
Direction of Induced Current (Fleming’s Right-Hand Rule):
- Stretch the right-hand thumb, forefinger, and middle finger so that they are mutually perpendicular.
- The forefinger points in the direction of the magnetic field.
- The thumb points in the direction of motion of the conductor.
- The middle finger then gives the direction of the induced current.
Conclusion:
Lenz’s Law shows that the induced current always acts in such a direction as to oppose the cause that produces it. This ensures that mechanical energy is converted into electrical energy, and no energy is produced without work being done.
Limitations / Note:
- If the induced current were in a direction that did not oppose the motion of the magnet, electrical energy would be obtained continuously without doing any work, which is impossible.
- Hence, Lenz’s Law is consistent with the principle of conservation of energy.
Key Points
Key Points: Force on a Current Carrying Conductor in a Magnetic Field
- A current-carrying conductor placed in a magnetic field experiences a force when the direction of current is not parallel to the magnetic field.
- The direction of force reverses when the direction of current or the direction of magnetic field is reversed, and no force acts when current flows parallel to the magnetic field.
Key Points: Simple D.C. Motor
Important Questions [22]
- On reversing the direction of the current in a wire, the magnetic field produced by it gets ______.
- Given below is a circuit to study the magnetic effect of electric current. ABCD is a cardboard kept perpendicular to the conductor XY. A magnetic compass is placed at the point P of the cardboard.
- A magnet kept at the centre of two coils A and B is moved to and fro as shown in the diagram. The two galvanometers show deflection. State with a reason whether :
- State the Direction in Which Current-carrying Rests
- Why Does a Current Carrying, Freely Suspended Solenoid Rest Along a Particular Direction?
- The Diagram Shows a Coil Wound Around a U Shape Soft Iron Bar Ab What is the Polarity Induced at the Ends a and B When the Switch is Pressed? Suggest One Way to Strengthen the Magnetic Field in the Electromagnet What Will Be the Polarities at a and B If the Direction of Current is Reversed in the Circuit?
- State Any Two Advantages of Electromagnets Over Permanent Magnets.
- If the strength of the current flowing through a wire is increased, the strength of the magnetic field produced by it ______.
- A copper conductor is placed over two stretched copper wires whose ends ate connected to a D.C. supply as shown in the diagram.
- State Two Ways to Increase the Speed of Rotation of a D.C. Motor.
- State two factors affecting the coil's rotation speed in a D.C. motor.
- Name a Common Device that Uses Electromagnets.
- In the Following Diagram an Arrow Shows the Motion of the Coil Towards the Bar Magnet.
- State one factor that affects the magnitude of induced current in an AC generator.
- Draw a Neat Labeled Diagram of an A.C. Generator
- Give two similarities an AC generator and a DC motor
- On which type of current do transformers work?
- Name the Transformer Used in the Power Transmitting Station of a Power Plant.
- What Type of Current is Transmitted from the Power Station?
- Name two factors on which the magnitude of an induced e.m.f. in the secondary coil depends.
- How is the E.M.F. Across Primary and Secondary Coils of a Transformer Related with the Number of Turns of the Coil in Them?
- Which Coil of a Step up Transformer is Made Thicker and Why?
Concepts [20]
- Oersted's Experiment
- Applications of Biot-Savart's Law > Magnetic Field due to a Finite Straight Current-Carrying Wire
- Right-hand Thumb Rule
- Applications of Biot-Savart's Law > Magnetic Field at the Centre of a Circular Loop
- Applications of Ampere’s Circuital Law > Magnetic Field of a Long Straight Solenoid
- Electromagnet
- Permanent Magnet
- Comparison of an Electro Magnet with a Permanent Magnet
- Advantages of an Electromagnet over a Permanent Magnet
- Uses of Electromagnet
- Force on a Current Carrying Conductor in a Magnetic Field
- Simple D.C. Motor
- Electromagnetic Induction
- Demonstration of the Phenomenon of Electromagnetic Induction
- Faraday's Explanation
- Faraday's Laws of Electromagnetic Induction
- A.C. Generator
- Frequency of an a.c. in Household Supplies
- Comparison Between A.C. Generator and D.C. Motor
- Transformers
