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प्रश्न
Explain, with the help of a suitable example, how we can show that Lenz's law is a consequence of the principle of conservation of energy.
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उत्तर
Lenz's law states that the polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it. The negative sign shown in equation `epsilon = -(d Ø_"g")/(d"t")` represents this effect.
Conservation of energy :
Suppose that the induced current was in the direction opposite to the one depicted in Fig. (a). In that case, the South-pole due to the induced current will face the approaching North-pole of the magnet. The bar magnet will then be attracted to the coil at an ever-increasing acceleration. A gentle push on the magnet will initiate the process and its velocity and kinetic energy will continuously increase without expending any energy. If this can happen, one could construct a perpetual-motion machine by a suitable arrangement. This violates the law of conservation of energy and hence can not happen. Now consider the correct case shown in Fig. (a). In this situation, the bar magnet experiences a repulsive force due to the induced current. Therefore, a person has to do work in moving the magnet. Where does the energy spent by the person go? This energy is dissipated by Joule heating produced by the induced current.
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संबंधित प्रश्न
State Lenz's law. Illustrate, by giving an example, how this law helps in predicting the direction of the current in a loop in the presence of a changing magnetic flux.
Describe a simple experiment (or activity) to show that the polarity of emf induced in a coil is always such that it tends to produce a current which opposes the change of magnetic flux that produces it.
Consider the situation shown in figure. If the switch is closed and after some time it is opened again, the closed loop will show ____________ .
Two circular loops of equal radii are placed coaxially at some separation. The first is cut and a battery is inserted in between to drive a current in it. The current changes slightly because of the variation in resistance with temperature. During this period, the two loops _______________ .
Consider the situation shown in figure. If the closed loop is completely enclosed in the circuit containing the switch, the closed loop will show _______________ .
Consider a metal ring kept (supported by a cardboard) on top of a fixed solenoid carrying a current I (Figure). The centre of the ring coincides with the axis of the solenoid. If the current in the solenoid is switched off, what will happen to the ring?
A conducting wire XY of mass m and neglibile resistance slides smoothly on two parallel conducting wires as shown in figure. The closed circuit has a resistance R due to AC. AB and CD are perfect conductors. There is a ˆ. magnetic field `B = B(t)hatk`.
- Write down equation for the acceleration of the wire XY.
- If B is independent of time, obtain v(t) , assuming v(0) = u0.
- For (b), show that the decrease in kinetic energy of XY equals the heat lost in R.
A metallic ring of mass m and radius `l` (ring being horizontal) is falling under gravity in a region having a magnetic field. If z is the vertical direction, the z-component of magnetic field is Bz = Bo (1 + λz). If R is the resistance of the ring and if the ring falls with a velocity v, find the energy lost in the resistance. If the ring has reached a constant velocity, use the conservation of energy to determine v in terms of m, B, λ and acceleration due to gravity g.
In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:
