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Alternating Current Notes
MAGNETIC FLUX
Magnetic flux. The magnetic flux through any surface placed in a magnetic field is the total number of magnetic lines of force crossing this surface normally. It is measured as the product of the component of the magnetic field normal to the surface and the surface area.
Magnetic flux is a scalar quantity, denoted by ϕ or ϕB.
If a uniform magnetic field B→passes normally
through a plane surface area A, as shown in Fig. 6.1(a), then the magnetic flux through this area is
ϕ = BA
If the field makes angle θ with the normal drawn to the area A, as shown in Fig. 6.1(b), then the
Fig. 6.1 . Magnetic flux through an area depends on its orientation w.r.t. the magnetic field.
component of the field normal to this area will be B cos θ, so that
ϕ = B cos θ × A
or ϕ = BAcosθ – B→.A→
Here the direction of vector A→ is the direction of the outward drawn normal to the surface.
In general, the field B→ over an area A may not be uniform. However, over a small area element dA→, the field B→ may be assumed to be uniform. As shown in Fig. 6.2, if θ is the angle between B→ and the normal drawn to area element d A→, then the component of B→ normal to d A→ will be B cos θ.
∴ Flux through area element d is
dϕ = B⊥ dA= B cos θ dA = BdA cos θ = B→.d A→
SI unit of magnetic flux. The SI unit of magnetic flux is weber (Wb). One weber is the flux produced when a uniform magnetic field of one tesla acts normally over an area of 1 nf.
1 weber = 1 tesla × 1 metre2
or 1 Wb = 1 Tm2
CGS unit of magnetic flux. The CGS unit of magnetic flux is maxwell (Mx). One maxwell is the flux produced when a uniform magnetic field of one gauss acts normally over an area ofl emf
1 maxwell = 1 gauss × 1 cm2
or 1 Mx = 1 G cm2
Relation between weber and maxwell
1 Wb = 1 T × 1 m2 = 104 G × 104 cm2
or 1 Wb = 108 maxwell.
Positive and negative flux. A normal to a plane can be drawn from either side. If the normal drawn to a plane points out in the direction of the field, then θ =0° and the flux is taken as positive. If the normal points in the opposite direction of the field, then θ = 180° and the flux is taken as negative.
Electromagnetic Induction Notes Class 12 Physics
ELECTROMAGNETIC INDUCTION: AN INTRODUCTION
tism are intimately connected. In the early part of the nineteenth century, the experiments of Oersted, Ampere and others established that moving charges (currents) produce a magnetic field. The converse effect is also true i.e., moving magnets can produce electric currents. In 1831, Michael Faraday in England and almost simultaneously Joseph Henry in the U.S.A. discovered that currents are produced in a loop of wire if a magnet is suddenly moved towards the loop or away from the loop such that the magnetic flux across the loop changes. The current in the loop lasts so long as the flux is changing. This phenomenon is called electromagnetic induction which means inducing electricity by magnetism.
The phenomenon of production of induced emf (and hence induced current) due to a change of magnetic flux linked with a closed circuit is called electromagnetic induction.
The phenomenon of electromagnetic induction is of great practical importance in daily life. It forms the basis of the present day generators and transformers. Modern civilisation owes a great deal to the discovery of electromagnetic induction.
Electromagnetic Induction & Alternating Current Notes Class 12 Physics
FARADAY’S EXPERIMENTS
3. Describe the various experiments performed by Faraday and Henry which ultimately led to the discovery of the phenomenon of electromagnetic induction.
Faraday’s experiments. The phenomenon of electromagnetic induction was discovered and understood on the basis of the following experiments performed by Faraday and Henry.
Experiment 1.Induced emf with a stationary coil and moving magnet. As shown in Fig. 6.4, take a circular coil of thick insulated copper wire connected to a sensitive galvanometer.
(i) When the N-pole of a strong bar magnet is moved towards the coil, the galvanometer shows a deflection, say to the right of the zero mark [Fig. 6.4 (ii)].
(ii) When the N-pole of the bar magnet is moved away from the coil, the galvanometer shows a deflection in the opposite direction [Fig. 6.4 (b)].
(iii) If the above experiments are repeated by bringing the S-pole of the magnet towards or away from the coil, the direction of current in the coil is opposite to that obtained in the case of N-pole.
(iv) When the magnet is held stationary anywhere near or inside the coil, the galvanometer does not show any deflection [Fig. 6.4 (c)].
Fig. 6.4 Induced emf with a moving magnet and stationary coil.
Explanation. When a bar magnet is placed near a coil, a number of lines of force pass through it. As the magnet is moved closer to the coil, the magnetic flux (the total number of magnetic lines of force) linked with the coil increases, an induced emf and hence an induced current is set up in the coil in one direction. As the magnet is moved away from the coil, the magnetic flux linked with the coil decreases, an induced emf and hence an induced current is set up in the coil in the opposite direction. As soon as the relative motion between the magnet and the coil ceases, the magnetic flux linked with the coil stops changing and so the induced current through the coil becomes zero.
Experiment 2. Induced emf with a stationary magnet and moving coil. Similar results as in experiment 1 are obtained if the magnet is held stationary and the coil is moved, as shown in Fig. 6.5. When the relative motion between the coil and the magnet is fast, the deflection in the galvanometer is large and when the relative motion is slow, the galvanometer deflection is small.
Fig. 6.5 Electromagnetic induction with a stationary magnet and moving coil.
Faster the relative motion between the magnet and the coil, greater is the rate of change of magnetic flux linked with the coil and larger is the induced current set up in the coil.
Experiment 3. Induced emf by varying current in the neighbouring coil. Fig. 6.6 shows two coils P and S wound independently on cylindrical support. The coil P, called the primary coil, is connected to a battery and a rheostat through a tapping key K. The coil S, called the secondary coil, is connected to a sensitive galvanometer.
(i) When the tapping key is pressed, the galvanometer shows a momentary deflection in one direction (Fig. 6.6). When the key is released, it again shows a momentary deflection but in the opposite direction.
Fig. 6.6 Electromagnetic induction by the varying current in the neighboring coil.
(ii) If the tapping key is kept pressed and a steady current flows through the primary coil, the galvanometer does not show any deflection.
(iii) As the current in the primary coil is increased with the help of the rheostat, the induced current flows in the secondary in the same direction as that at the make of the primary circuit.
(iv) As the current in the primary coil is decreased, the induced current flows in the same direction as that at the break of the primary circuit.
(v) The deflections in the galvanometer become larger if we use a cylindrical support made of iron.
Explanation. When a current flows through a coil, a magnetic field gets associated with it. As the primary circuit is closed, the current through it increases from zero to a certain steady value. The magnetic flux linked with the primary and hence with the secondary also increases. This sets up an induced current in the secondary coil in one direction. As the primary circuit is broken, the current decreases from the steady value to zero, the magnetic flux through the secondary coil decreases. An induced current is set up in the secondary coil but in the opposite direction. When a steady current flows in the primary coil, the magnetic flux linked with the primary coil does not change and no current is induced in the secondary coil.
From these experiments, we may conclude that:
1. Whenever the magnetic flux linked with a closed circuit changes, an induced emf and hence an induced current is set up in it.
2. The higher the rate of change of magnetic flux linked with the closed circuit, the greater is the induced emf or current.
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