Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
In this problem a relation is established between induced current, power lost and velocity acquired by freely falling ring.
The magnetic flux linked with the metallic ring of mass m and radius l ring being horizontal falling under gravity in a region having a magnetic field whose z-component of magnetic field is Bz = B0(1 + λz) is `phi = vecB_z.vecA = B_o (1 + λz).pil^2`
The angle between `vecB` and `vecA` is 0°
`ε = d/(dt) [B_o (1 + λz)]pil^2`
`IR = (B_opil^2)[0 + λ (dz)/(dt)]`
`I = (B_opiλl^2)/R (dz)/(dt) = (B_opiλl^2)/R v`
Energy lost = `I^2R = (B_o^2pi^2λ^2l^4)/R^2 v^2R`
Energy lost = `(B_o^2pi^2λ^2l^4v^2)/R`
The energy must come from decrease in P.E = `mg (dz)/(dt) = mgv`
∴ `mgv = (B_o^2pi^2λ^2v^2l^4)/R`
`v = (mgR)/(B_o^2pi^2λ^2l^4)` or `(mgR)/((pil^2λB_o)^2)`
It is the required relation.
APPEARS IN
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.
Use Lenz’s law to determine the direction of induced current in the situation described by the figure:
A wire of irregular shape turning into a circular shape.
Show that Lenz's law is a consequence of conservation of energy.
A short magnet is moved along the axis of a conducting loop. Show that the loop repels the magnet if the magnet is approaching the loop and attracts the magnet if it is going away from the loop.
A pivoted aluminium bar falls much more slowly through a small region containing a magnetic field than a similar bar of an insulating material. Explain.
Consider the situation shown in figure. If the switch is closed and after some time it is opened again, the closed loop will show ____________ .
A bar magnet is released from rest along the axis of a very long, vertical copper tube. After some time the magnet ____________ .
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 _______________ .
Lenz’s law is a consequence of the law of conservation of ______.
Which of the following statements is not correct?
Consider a magnet surrounded by a wire with an on/off switch S (Figure). If the switch is thrown from the off position (open circuit) to the on position (closed circuit), will a current flow in the circuit? Explain.
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 long solenoid ‘S’ has ‘n’ turns per meter, with diameter ‘a’. At the centre of this coil we place a smaller coil of ‘N’ turns and diameter ‘b’ (where b < a). If the current in the solenoid increases linearly, with time, what is the induced emf appearing in the smaller coil. Plot graph showing nature of variation in emf, if current varies as a function of mt2 + C.
Predict the direction of induced current in the situation described by the following figure.
Predict the direction of induced current in the situation described by the following figure.
Predict the direction of induced current in the situation described by the following figure.
Use Lenz’s law to determine the direction of induced current in the situation described by the figure.
A circular loop being deformed into a narrow straight wire.
