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.
RELATED QUESTIONS
Define coefficient of 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 20 A in 0.5 s, what is the change of flux linkage with the other coil?
Find the mutual inductance between the circular coil and the loop shown in figure.
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 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 dimensions of self or mutual inductance are given as ______.
In mutual induction, the main current remains same because ____________.
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 ____________.
A current I = 10 sin (50 π t) ampere is passed in the first coil which induces a maximum e.m.f. of 5 π volt in the second coil. The mutual inductance between the coils is ______.
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)
A coil of radius 'r' is placed on another coil (whose radius is 'R' and current flowing through it is changing) so that their centres coincide. (R>>r) if both the coils are coplanar then the mutual inductance between them is proportional to ______.
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)
The mutual inductance between two coils is 0.09 henry. If the current in the primary coil changes from 0 to 20 A in 0.006 s, the e.m.f. induced in the secondary coil at that instant is ____________.
The mutual inductance of a pair of coils is 0.75 H. If current in the primary coil changes from 0.5 A to zero in 0.01 s, find average induced e.m.f. in secondary coil ______.
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)
Two coils having self inductances L1 = 75 mH and L2 = 55 mH are coupled with each other. The coefficient of coupling (K) is 0. 75. Calculate the mutual inductance (M) of the two coils
Two planar concentric rings of metal wire having radii r and r2 (r₁ > r2) are placed in air. The current I is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( μο = permeability of free space) ______.
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 ______.
