Advertisements
Advertisements
Question
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?
Advertisements
Solution
Number of turns on the solenoid = 15 turns/cm = 1500 turns/m
Number of turns per unit length, n = 1500 turns
The solenoid has a small loop of area, A = 2.0 cm2
= 2 × 10−4 m2
Current carried by the solenoid changes from 2 A to 4 A.
∴ Change in current in the solenoid, di = 4 − 2 = 2 A
Change in time, dt = 0.1 s
Induced emf in the solenoid is given by Faraday’s law as:
`"e" = ("d"phi)/("dt")` ........(1)
Where,
`phi` = Induced flux through the small loop = BA ...........(2)
B = Magnetic field = `mu_0"ni"` .....(3)
μ0 = Permeability of free space
= 4π × 10−7 H/m
Hence, equation (1) reduces to:
`"e" = "d"/("dt")("BA")`
= `"A"mu_0"n" xx (("di")/("dt"))`
= `2 xx 10^-4 xx 4pi xx 10^-7 xx 1500 xx 2/0.1`
= 7.54 × 10−6 V
Hence, the induced voltage in the loop is 7.54 × 10−6 V.
APPEARS IN
RELATED QUESTIONS
If the radius of a sphere is doubled without changing the charge on it, then electric flux originating from the sphere is ______.
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.
Explain self induction and mutual induction
Explain the phenomenon of mutual induction.
A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 10 A in 0.2 s, what is the change of flux linkage with the other coil?
A long solenoid of length l, cross-sectional area A and having N1 turns (primary coil), has a small coil of N2 turns (secondary coil) wound about its center. Determine the Mutual inductance (M) of the two coils.
The mutual inductance of two coils is 10 mH. If the current in one of the coil changes from 5 A to 1 A in 0.2 s, calculate the emf induced in the other coil. Also calculate the induced charge flowing through the coil if its resistance is 5 Ω.
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 ______.
Two different wire loops are concentric and lie in the same plane. The current in the outer loop (I) is clockwise and increases with time. The induced current in the inner loop.
The coefficient of mutual inductance is 2H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A and 3A. The time required for the change of current 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 ______.
An emf of 91 mV is induced in the windings of a coil when the current in o nearby coil is increasing at the rate of 1.3 A/s. what is the mutual inductance (M) of the two coils in mH?
Write the S.I. unit of mutual inductance.
The mutual inductance of a pair of adjacent coils is 1.5 H. If the current is one coil changes from 5 A to 10 A in 0.1 s, the rate of change of magnet flux linkage is ______.
A rectangular coil of wire 50 turn each of area 6 x 10-4 m2 is freely suspended in a field of 3 x 10-2 Wb / m2. Calculate the current flowing through the coil when it deflects through 60°, when torsional constant is 3.82 x 10-6 SI unit.
State and define the SI unit of mutual inductance.
