Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10−3 s. How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.
Consider two concentric circular coils, one of radius r1 and the other of radius r2 (r1 < r2) placed coaxially with centers coinciding with each other. Obtain the expression for the mutual inductance of the arrangement.
A coil of self-inductance 2.5H and resistance 20Ω is connected to a battery of emf 120V having the internal resistance of 5 n. Find:
1) The time constant of the circuit.
2) The current in the circuit in steady state
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.
In mutual induction, the main current remains same because ____________.
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)
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.
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 ____________.
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 ______.
Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon the ______.
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?
A plane loop is shaped in the form as shown in figure with radii a = 20 cm and b = 10 cm and is placed in a uniform time varying magnetic field B = B0 sin ωt, where B0 = 10 mT and ω = 100 rad/s. The amplitude of the current induced in the loop if its resistance per unit length is equal to 50 × 10-3 Ω/m. The inductance of the loop is negligible is ______ A.
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 ______.
Which relation defines mutual inductance using the flux linkage \[N_2\phi_{21}\] and current \[I_1\] ?
What do \[L_1\] and \[L_2\] represent in \[M=K\sqrt{L_1L_2}\] ?
What is the effect of a larger cross-sectional area of the coils on mutual inductance?
What is the magnetic field at the centre of the outer large coil when it carries current \[I_2\] ?
Which definition relates the flux through the inner coil to the current in the outer coil?
What is the mutual inductance of a small circular coil of radius \[r_1\] at the centre of a large circular coil of radius \[r_2\] when \[r_1\ll r_2\] ?
