A wire 88 cm long is bent into a circular loop and kept with its plane

1.	A wire 88 cm long is bent into a circular loop and kept with its plane perpendicular to a magnetic field of induction 2.5 Wb/m2. Within 0.5 second, the coil is changed to a square and the magnetic induction is increased by 0.5 Wb/m2.. Calculate the emf induced in the wire.
Answer» Data: l = 88 cm, B = 2.5 Wb/m², B = 3 Wb/m², ∆t = 0.5 s For the circular loop, l = 2πr ∴ r = \(\cfrac{l}{2\pi}\) = \(\cfrac{88}{2\times(22/7)}\) = 14 cm = 0.14 m Area of the circular loop, A_i = πr² = \(\cfrac{22}7\)(0.14)² = 0.0616 m² Initial magnetic flux, Φ_i = A_iB_i = 0.0616 × 2.5 = 0.154 Wb For the square loop, length of each side = \(\cfrac{88}4\) cm = 22 cm = 0.22 m⁴ Area of the square loop, A_f = (0.22)² = 0.0484 m² ∴ Final magnetic flux, Φ_f = A_fB_f = 0.0484 × 3 = 0.1452 Wb Induced emf, e = – \(\cfrac{Φ_f−Φ_1}{Δt}\) = \(\cfrac{Φ_1−Φ_f}{Δt}\) ∴ e = \(\cfrac{0.154 - 0.1452}{0.5}\) =8.8 x 10^-3 x 2 = 1.76 × 10^-2 V

A wire 88 cm long is bent into a circular loop and kept with its plane perpendicular to a magnetic field of induction 2.5 Wb/m2. Within 0.5 second, the coil is changed to a square and the magnetic induction is increased by 0.5 Wb/m2.. Calculate the emf induced in the wire.

Answer»

Data: l = 88 cm,

B = 2.5 Wb/m²,

B = 3 Wb/m²,

∆t = 0.5 s

For the circular loop, l = 2πr

∴ r = \(\cfrac{l}{2\pi}\) = \(\cfrac{88}{2\times(22/7)}\) = 14 cm = 0.14 m

Area of the circular loop, A_i = πr²

= \(\cfrac{22}7\)(0.14)² = 0.0616 m²

Initial magnetic flux, Φ_i = A_iB_i

= 0.0616 × 2.5 = 0.154 Wb

For the square loop, length of each side

= \(\cfrac{88}4\) cm = 22 cm = 0.22 m⁴

Area of the square loop, A_f = (0.22)²

= 0.0484 m²

∴ Final magnetic flux, Φ_f = A_fB_f

= 0.0484 × 3 = 0.1452 Wb

Induced emf, e = – \(\cfrac{Φ_f−Φ_1}{Δt}\) = \(\cfrac{Φ_1−Φ_f}{Δt}\)

∴ e = \(\cfrac{0.154 - 0.1452}{0.5}\) =8.8 x 10^-3 x 2

= 1.76 × 10^-2 V

Discussion

No Comment Found

Related InterviewSolutions

A current through a coil of self inductance 10 mH increases from 0 to 1 A in 0.1 s. What is the induced emf in the coil?(A) 0.1 V (B) 1 V (C) 10 V (D) 0.01 V
A toroidal coil has an inductance of 47 mH. Find the maximum self-induced emf in the coil when the current in it is reversed from 15 A to -15 A in 0.01 s.
A bar magnet moves vertically down, approaching a circular conducting loop in the xy plane. The direction of the induced current in the loop (looking down the z-axis) is(A) anticlockwise (B) clockwise (C) alternating (D) along negative z-axis.
A flexible wire of irregular shape, abcd, as shown in the figure, turns into a circular shape w,hen placed in a region of magnetic field which is directed normal to the plane of the loop away from the reader. Predict the direction of the induced current in the wire.
While sitting a lawn, Ashok and his friends saw that a bird was sitting on high voltage wire. They observed that when a current passed through the wire, the bird sitting on it flew away. People along with both of them gave their opinions and reasons for it, but nobody was able to give a proper balanced option, but in the last Ashok explained the reason behind it. (a) What are the value displayed by Ashok ?(b) Why as soon as the current passed through a high voltage wire, the bird sitting on it flew away ?
The electric current flowing in a wire in the direction from B to A is decreasing. Find out the direction of the induced current in the metallic loop kept above the wire as shown.
Isabella used an induction stove and explains to her neighbour that due to shortage of LPG one must utilize other sources that are available to produce heat energy; being a Physics teacher Isabella, explains that the oil companies are trying their best to meet the demands for LPG and that as a good citizen one must use other sources wherever feasible. Isabella uses an induction stove having a value of 7 H inductor and the flow of current from 10 A to 7 A in x 10-2 seconds. (i) In the above, what is the quality, you find in the Physics teacher ?(ii) Calculate the emf generated in the above ?
Predict the polarity of the plate A of the capacitor, when a magnet is moved towards it, as shown in the figure.
Predict the directions of induced current in metal rings 1 and 2 lying in the same plane where current I in the wire is increasing continuously.
While checking with metal detector at the airport, Imran was asked to take out the material from his pant and shirt pockets. Imran got annoyed and argued with airport security asking the reasons for such procedure. He was conveyed that as per security rule, the passengers and their luggage will be checked for security check to ensure safe travel. (i) What is the value that imparts us in the above scenario ? (ii) Briefly explain the working principle of a metal detector