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Physics Topics are often described using mathematical equations, making them precise and quantifiable.
How do you Determine the Direction of the Induced Current?
When a current carrying wire is placed in a magnetic field, it is deflected, i.e., a motion is generated. An opposite phenomenon was first observed by Michael Faraday. He saw that, if a closed wire loop is moved in a magnetic field, an electric current is generated in that loop as long as the motion continues.
Definition: If there is a relative motion between a magnetic field and a conductor, an electromotive force is generated in the conductor. It is called induced electromotive force.
It should be noted carefully that, to get electric current from this induced emf, the conductor should be in the form of a closed circuit. This is because, the resistance of an open circuit is infinite and hence, in spite of the presence of induced emf, no current passes through the conductor.
Definition: If there is a relative motion between a magnetic field and a closed circuit conductor, the current flowing through that conductor is known as induced current. Electromagnetic induction: The phenomenon involving the generation of electrical energy due to relative motion between a magnetic field and a conductor is called electromagnetic induction.
Experimental Demonstration : Magnitude And Direction of Induced Current
Induced current with the help of a magnet: In Fig., C is a circular coil having one or more turns. M is a permanent magnet kept along the axis of C. G is a galvanome-ter connected to C :
By observing the deflection of the pointer in G towards left or right, the direction of current in the coil C (i.e., anticlockwise or clockwise) can be determined. Again, noting the extent of deflection of the pointer (i.e., low or high), the magnitude of current, whether low or high, can be ascertained.
For different motions of the magnet along the axis of the coil, the directions of induced current through the coil are given in the following table.
Relative position of the coil and the magnet | Relative motion of the coil and the magnet | Direction of induced current (viewed from the side of the magnet) |
North pole(N) of the magnet facing coil C[Fig.] | The magnet M moves towards the centre of the coil[Fig.] | Anticlockwise[Fig.] |
The magnet M moves away from the centre of the coil | Clockwise | |
South pole (S) of the magnet facing coil C. | The magnet M moves towards the centre of the coil. | Clockwise |
The magnet M moves from the centre of the coil | Anticlockwise |
Note that, no induced current is noticed in the coil when
- the magnet is at rest,
- the magnet rotates about its own axis or
- both the magnet and this coil move in such a way that no relative motion exists between them.
Keeping the magnet at rest, if the coil is moved towards or away from the magnet, the same results will be obtained.
Direction of the induced electromotive force: This direction depends on
- the nature of the magnetic pole facing the conductor and
- the direction of motion of the magnet with respect to the conductor.
Magnitude of the induced electromotive force:
- Increases with increase in the relative velocity between the coil and the magnet.
- Increases with increase in pole-strength of the magnet.
- Increases with increase in the number of turns of the coil.
Magnitude and direction of the induced current:
- Direction is identical with the direction of induced electro-motive force.
- Magnitude is directly proportional to the magnitude of the induced emf.
- Inversely proportional to the resistance of the coil.
Note that, induced electromotive force does not depend on the resistance of the circuit. In an open circuit, the resistance is infinite, hence no current passes but the induced emf associated with the circuit does exist.
Current induced with the help of current carrying conducting coil or current carrying solenoid: A current carrying circular coil or a current carrying solenoid is equivalent to a permanent magnet. The rule for determination of their poles are
1. if the current viewed from a face be anticlockwise, that face acts as north pole (N) and
2. if the current viewed from a face be clockwise, that face acts as south pole (S). So, if a circular current carrying coil or a current carrying solenoid be used instead of the magnet M shown in Fig., the same experimental result will be obtained. Two more important facts should be noted:
- With increase in the current through the circular coil or solenoid, the strength of the magnetic field increases.
- If the direction of current through the circuit is reversed, magnetic polarity is also reversed.
Current induced with the help of static electrical Circuits: In Fig., S is a circular coil with one or more turns. A galvanometer G is connected with it. From this galvanometer, the magnitude and direction of the induced current can be determined. P is another co-axial circular coil connected with an electrical circuit. 5 is a battery and a key K is used to switch on or off the circuit. Again, with the help of the rheostat Rh, current through the circuit can be increased or decreased.
Now, if the circuit P be switched ‘on’ or if the current in the circuit is increased rapidly, magnetic field also increases considerably. It is similar to the situation when a magnet is moved towards the coil S swiftly. So, the results of two phenomena: ‘increase of current in the circuit P’ and ‘relative motion between the coil S and the magnetic field’ are identical. Naturally, if the circuit P is switched ‘off’ suddenly or if the current in the circuit be decreased rapidly, the effective relative velocity becomes just opposite to the former case.
Observation: If the current through the coil P be increased or decreased in different ways by means of the key K and the rheostat Rh, the induced current found in the coil S will be as described below:
Current in the coil P | Observations |
Circuit P is suddenly switched on. | A momentary current is induced in the coil S; the direction of this induced current is opposite to that in the coil P. |
Circuit P is suddenly switched off. | A momentary current is induced in the coil S; this induced current is in the same direction as that in the coil P. |
Current in the coil P is gradually increased or decreased at a uniform rate. | A constant current is induced; this induced current is opposite in direction during increase and is in the same direction during decrease of current. |
Current through the coil P is zero or of a steady value. | No current is induced in the coil S. |
Primary and secondary coils: in the experiment shown in Fig. , the current through the coil P is the cause of electromagnetic induction and this coil is called the primary coil. On the other hand, the current in the coil S is the result of electromagnetic induction and this coil is called the secondary coil.
Magnetic Induction And Flux
From the discussion of magnetism we know that, if a magnetic material is placed in an external magnetic field, it gets magnetically induced. This magnetic induction is a vector quantity, and the most convenient way to specify its magnitude and direction is to draw lines of induction through that substance. If the magnetic induction is greater at a place, lines of induction get crowded there. Moreover, the direction of lines of induction is to be represented according to the direction of magnetic induction at every point. From this we can define magnetic induction as follows:
Definition: The number of lines of induction passing nor-mally through unit area surrounding a point inside a sub-stance is called magnetic induction at that point.
Magnetic induction is a vector quantity, its symbol is \(\vec{B}\). This vector is identical to the magnetic field \(\vec{B}\) described in the chapter ‘Electromagnetism’.
Usually the lines of induction passing through any medium are called lines of force. These continuous lines of force passing through a medium can be imagined as a kind of stream. This stream is comparable with the flow of water. We know that, in case of water flow, the rate of flow of water can be obtained from the mass of water, passing through any cross-section. Magnetic flux can be defined from this analogy.
Definition: The number of lines of induction passing nor-mally through any surface placed in a magnetic field is called the magnetic flux linked with that surface.
Magnetic flux is a scalar quantity, and its symbol is ϕ.
Let the area of a surface placed in a uniform magnetic field be A [Fig.], If the magnetic induction \(\vec{B}\) is inclined at an angle θ with the normal to the surface, the component of \(\vec{B}\) in the direction of that normal is Bcosθ (magnitude of \(\vec{B}\) is B).
Hence according to the definition, magnetic flux,
ϕ = BA cosθ = \(\vec{B}\) ᐧ \(\vec{A}\) = \(\vec{B}\) ᐧ \(\hat{n}\)A where \(\hat{n}\) is a unit vector normal to the surface.
For a finite surface, we first consider the magnetic flux through an infinitesimal area d\(\vec{A}\). The magnetic flux across this area,
dϕ = \(\vec{B}\) ᐧ d\(\vec{A}\)
A finite surface A can be assumed as the summation of such infinitesimal elements and the magnetic flux through the total surface area,
ϕ = \(\int_S \vec{B} \cdot d \vec{A}\)
Special cases:
i) If the lines of induction are along the surface, then θ = 90° and hence ϕ = 0 .
ii) If the lines of induction are perpendicular to the surface, θ = 0° and hence ϕ = BA . In this case, B = \(\frac{\phi}{A}\) = magnetic flux linked with unit area.
Thus, magnetic induction \(\vec{B}\) is also called magnetic flux density. According to Fig., this flux is positive.
iii) If θ = 180°, ϕ = -BA i.e., flux is negative.