Advertisements
Advertisements
Question
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.
Advertisements
Solution
Length of the rod, l = 1 m
Angular frequency, ω = 400 rad/s
Magnetic field strength, B = 0.5 T
One end of the rod has zero linear velocity, while the other end has a linear velocity of lω.
Average linear velocity of the rod, `"v" = ("l"omega + 0)/2`
= `("l"omega)/2`
Emf developed between the centre and the ring,
e = Blv
= `"Bl"(("l"omega)/2)`
= `("Bl"^2omega)/2`
= `(0.5 xx (1)^2 xx 400)/2`
= 100 V
Hence, the emf developed between the centre and the ring is 100 V.
APPEARS IN
RELATED QUESTIONS
Explain the meaning of the term mutual inductance.
Draw a necessary arrangement for winding of primary and secondary coils in a step-up transformer. State its underlying principle and derive the relation between the primary and secondary voltages in terms of number of primary and secondary turns. Mention the two basic assumptions used in obtaining the above relation.
The current flowing through an inductor of self inductance L is continuously increasing. Plot a graph showing the variation of Magnetic potential energy stored versus the current.
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?
The current in a long solenoid of radius R and having n turns per unit length is given by i= i0 sin ωt. A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid ant the coil.
A solenoid of length 20 cm, area of cross-section 4.0 cm2 and having 4000 turns is placed inside another solenoid of 2000 turns having a cross-sectional area 8.0 cm2 and length 10 cm. Find the mutual inductance between the solenoids.
A pair of the adjacent coil has a mutual inductance of 1.5 H. If the current in one coil varies from 0 to 20 A in 0.5 s, what is the change of flux linked with the other coil.
The dimensions of self or mutual inductance are given as ______.
In an induction coil, the coefficient of mutual inductance is 6 henry. If a current of 10 ampere in the primary coil is cut-off in `1/1500"s"`, the e.m.f. at the terminals of the secondary coil will be ____________.
An alternating current of frequency 200 rad/s and peak value 1 A is applied to the primary of a transformer. If the coefficient of mutual induction between the primary and the secondary is 1.5H, then the voltage induced in the secondary will be approximately (π = 2217)
Alternating current of peak value `(2/pi)` ampere flows through the primary coil of transformer. The coefficient of mutual inductance between primary and secondary coil is 1 H. The peak e.m.f. induced in secondary coil is ______. (Frequency of a.c. = 50 Hz)
Two coils P and Q have mutual inductance 'M' H. If the current in the primary is I = I0 sin `omega`t, then the maximum vlaue of e.m.f. indued in coil Q is ____________.
Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 > > R2, the mutual inductance M between them will be directly proportional to ______.
Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to ______.
A toroid is a long coil of wire wound over a circular core. The major radius and cross-sectional radius of the toroid are R and r, respectively. The coefficient of mutual induction of the toroid is ______.
(The magnetic field in it is uniform, N = number of turns, R >> r, μ0 = permeability of free space)
State and define the SI unit of mutual inductance.
The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A to 3 A. The time required for the change of current is ______.
The mutual inductance between a primary and secondary circuit is 0.4 H and the resistance in these circuits are \[20\Omega\] and \[4\Omega\] respectively. To produce a current of 0.5 A in the secondary, current in the primary must be changed at the rate of ______.
