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प्रश्न
State Lenz’s Law.
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उत्तर १
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)]
उत्तर २
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.
Notes
Students can refer to the provided solutions based on their preferred marks.
संबंधित प्रश्न
State Faraday's laws of electromagnetic induction.
In the following diagram an arrow shows the motion of the coil towards the bar magnet.
(1) State in which direction the current flows, A to B or B to A?
(2) Name the law used to come to the conclusion.
- How would you demonstrate that a momentary current can be obtained by the suitable use of a magnet, a coil of wire and a galvanometer?
- What is the source of energy associated with the current obtained in part (a)?
- Describe briefly one way producing an induced e.m.f?
- State one factor that determines the magnitude of induced e.m.f. in part (a) above.
- What factor determines the direction of induced e.m.f. in part (a) above?
In which of the following case does the electromagnetic induction occur?
A conductor is moved in a varying magnetic field. Name the law which determines the direction of current induced in the conductor.
What is Lenz’s law?
The direction of induced current is obtained by ______.
The diagram in shows a coil of several turns of copper wire near a magnet NS. The coil is moved in the direction of arrow shown in the diagram.
- In what direction does the induced current flow in the coil?
- Name the law used to arrive at the conclusion in part (i).
- How would the current in coil be altered if
- the coil has twice the number of turns,
- the coil was made to move three times fast?
Explain the principle, construction and working of a dc motor.
Faraday's law is the consequence of conservation of ______
An electron moves on a straight line path XY as shown. The abed is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil?
A coil of 25 turns is pulled in 0.05 s between the poles of a magnet, where its area includes `21 xx106-6 "Wb" "to" 1 xx 10^-6 "Wb"`. The average e.m.f. is ______.
In a coil of resistance 150 `Omega`, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is ____________.
Magnetic flux passing through a coil is initially 6 x 10-4 Wb. It reduces to 10 % of its original value in 't' second. If the e.m.f. induced is 0.54 mV then 't' in second is ____________.
A magnet is moved towards a coil (i) quickly (ii) slowly. The induced potential difference.
A.C generator works on the principle of ____________.
Fleming’s left hand and Right hand rules are used in ____________.
A D.C generator works on the principle of ____________.
The laws of induction were given by ______.
Two vectors `vec"A"` and `vec"B"` have equal magnitudes. If magnitude of `vec"A"` + `vec"B"` is equal to two times the magnitude of `vec"A"` - `vec"B"`, then the angle between `vec"A"` and `vec"B"` will be ______.
For which angle between two equal vectors `vec"A"` and `vec"B"` will the magnitude of the sum of two vectors be equal to the magnitude of each vector?
Two positively charged particles each having charge Q and are d distance apart. A third charge is introduced in midway on the line joining the two. Find nature and magnitude of third charge, so that the system is in equilibrium ______.
A conductor in the form of a circular arc of the radius of curvature R subtends an angle Ø at its centre of curvature. If the current in the conduct is I, the magnetic induction at the centre of curvature is ______.
A circular loop is placed in a uniform magnetic field. The total number of magnetic field lines passing normally through the plane of the coil is called ______.
Name the principle of AC generator.
State the use of the principle of electromagnetic induction.
State two factors on which the magnitude of induced e.m.f. in a coil depend.
Explain how does the Lenz's law show the conservation of energy in the phenomenon of electromagnetic induction.
