Question: On what factors does the mutual inductance depend? Find an expression.
Answer:
Consider two coxial solenoids of equal lengths. Let a current is flowing in solenoid 1. Magnetic field inside solenoid 2
B1 = µon1i1
Flux in the inner solenoid of N2 turns = Φ21 = N2B1A = l.n2B1A
N2 =n2 . l
Φ21 = µon1n2lAi1
Φ21 = M21 i1
Where M21 = µon1n2lA is called mutual inductance of secondary coil with respect to the primary coil.
Question: On what factors does the self inductance of a coil depend? Find an expression.
Answer: Self inductance of a coil depends on the number of terns, length and area of cross section.
Magnetic field inside solenoid = u.ni
Flux in N turns = Φ = NBA
Φ = NµonAi
but N = n.l
Φ = µon2lAi
Φ = Li
L= u. N2A/l
n=N/l
L= u. n2A.l
Question: What is self induction?
Answer: an EMF is generated in a coil when its current changes. It opposite the change in current of the solenoid. It is known as back emf. This phenomenon is called self induction.
Question Define self inductance and write its SI unit.
Answer consider a current is passing through a solenoid. Flux in the solenoid is proportional to the current in it. The self inductance L of solenoid is equal to the flux linked with it when a unit current is passing.
Self inductance can also be defined as: EMF induced in the solenoid, when the rate of change of current in it is unity.
The SI unit of self inductance is Webber per ampere that is Henry H.
Qn. Define mutual induction and mutual inductance.
Answer:
Mutual induction. when current in a coil changes, then the magnetic flux Φ linked to a nearby coil also changes and hence an EMF is induced in that coil. This phenomenon is called mutual induction.
Mutual inductance M
The magnetic flux linked to the secondary coil is proportional to the current in the primary coil Φs= Msp.ip
Msp = a constant of proportionality known as the mutual inductance of secondary coil with respect to the primary coil
Msp. = Φs if ip = 1A
Mutual inductance is equal to the magnetic flux linked to the secondary coil when electric current in the primary coil is 1 ampere.
The SI unit of mutual inductances Henry(H). It is equal to one 1 Webber per ampere.
Other definition of Mutual inductance
If current in a primary coil is changing then
EMFs = dΦs/dt = Msp.dip/dt
If dip/dt= 1A/s then EMFs = Msp
So we define mutual inductance as the magnetic flux linked to the secondary coil when the rate of change of current in the primary coil is 1 ampere per second.
Qn. Find expression for motional EMF.
Answer: When a conducting rod of length L moves perpendicular to a magnetic field B with speed v then an EMF is induced in it given by EMF = BvL
If magnetic field makes an angle with the length of rod then EMF = BvL.sinθ
Lorentz force on a charge q at one end = qvB. Due to this force, the charge moves to the other end of conductor of length L
work done = EMF xq
and Work done = Force.displacement
Hence emf.q = qvB.L
emf = BvL
Special Case: when a rod is being rotated in a circle, keeping it's one end at the centre, then EMF = BwL2/2
6.7 A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s-1, at right angles to the horizontal component of the earth’s magnetic field, 0.30 × 10–4 Wb m–2.
(a) What is the instantaneous value of the emf induced in the wire?
(b) What is the direction of the emf?
6.5 A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s–1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
6.10 A jet plane is travelling towards west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the Earth’s magnetic field at the location has a magnitude of 5 × 10–4 T and the dip angle is 30°.
Qn. State Lenz's Law
The polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.
Example 6.4 Figure 6.7 shows planar loops of different shapes moving out of or into a region of a magnetic field which is directed normal to the plane of the loop away from the reader. Determine the direction of induced current in each loop using Lenz’s law.
Qn. Predict the polarity of the capacitor in the situation described by Fig.
Qn. 6.1 Predict the direction of induced current in the situations described by the following Figs.
6.2 Use Lenz’s law to determine the direction of induced current in the situations described by Fig.:
(a) A wire of irregular shape turning into a circular shape;
(b) A circular loop being deformed into a narrow straight wire.
Qn. Mention any two methods for electromagnetic induction?
Ans. 1. By relative motion between a magnet and a coil.
2. By changing current in a coil, a current is induced in the neighbouring coil.
Qn. State faraday's laws of electromagnetic induction.
- Whenever magnetic flux linked with a coil changes a current is induced in it.
- The induced current lasts as long as the change in flux takes place.
- The magnitude of induced EMF is equal to the time rate of change of the magnetic flux. EMF = dΦ/dt
for coil of N turns emf = N.dΦ/dt
6.3 A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
6.5 A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad/s about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
MAGNETIC FLUX
The magnetic flux through a plane of area A placed in a uniform magnetic field B can be written as
ΦB = B . A = BA cos θ
where θ is the angle between B and A.
For a curved surface
ΦB = ∑ B.A
The SI unit of magnetic flux is weber (Wb) or tesla.metersquared (T.m2 ). Magnetic flux is a scalar quantity.
1. State Faraday's law of electromagnetic induction.
8. A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s–1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
1. A jet plane is travelling towards west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the Earth’s magnetic field at the location has a magnitude of 5 × 10–4 T and the dip angle is 30°.
2. A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s–1, at right angles to the horizontal component of the earth’s magnetic field, 0.30 × 10–4 Wb m–2 .
(a) What is the instantaneous value of the emf induced in the wire?
(b) What is the direction of the emf?
(c) Which end of the wire is at the higher electrical potential?
3. A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad/s about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre of the ring.
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