Plot a Graph Showing the Variation of Magnetic Flux and Induced Emf as a Function of Time. - Physics


A square loop MNOP of side 20 cm is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the figure. The loop is pulled with a constant velocity of 20 cm s−1 till it goes out of the field.

(i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist?

(ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time.



(i)The direction of induced current in the loop as it goes out is depicted in the figure below.

The current will persist till the entire loop comes out of the field. Hence, we have

`t=d/v=(20 cm)/(20 `

Hence, the current will persist for 1 second.

(ii)The magnetic flux in the coil when it is inside the field is constant. This maximum flux is given as Φ = Bla (a is the side of the square loop). This flux will start dropping once the loop comes out of the field and will be zero when it is completely out of the field.

The e.m.f. induced in the coil when it is inside the field is zero as the flux is not changing. When the loop just comes out of the field, the flux change is maximum and the e.m.f. induced is `e=(dphi)/dt=-Bl(db)/(dt)=-Blv` This e.m.f remains constant till the entire loop comes out. When the loop is completely out of the field, the e.m.f. drops to zero again.

Concept: Magnetic Flux
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2014-2015 (March) Panchkula Set 3

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Ram is a student of class X in a village school. His uncle gifted him a bicycle with a dynamo fitted in it. He was very excited to get it. While cycling during night, he could light the bulb and see the objects on the road. He, however, did not know how this device works. he asked this question to his teacher. The teacher considered it an opportunity to explain the working to the whole class.

Answer the following questions:
(a) State the principle and working of a dynamo.

(b) Write two values each displayed by Ram and his school teacher.

The current flowing through an inductor of self inductance L is continuously increasing. Plot a graph showing the variation of

Magnetic flux versus the current

Draw a schematic sketch of an ac generator describing its basic elements. State briefly its working principle. Show a plot of variation of

(i) Magnetic flux and

(ii) Alternating emf versus time generated by a loop of wire rotating in a magnetic field.

A rectangular coil having 60 turns and area of 0.4m2 is held at right angles to a uniform magnetic field of flux density 5 × 10-5T. Calculate the magnetic flux passing through it.

A metallic loop is placed in a nonuniform magnetic field. Will an emf be induced in the loop?

An inductor is connected to a battery through a switch. Explain why the emf induced in the inductor is much larger when the switch is opened as compared to the emf induced when the switch is closed.

Figure shows a horizontal solenoid connected to a battery and a switch. A copper ring is placed on a frictionless track, the axis of the ring being along the axis of the solenoid. As the switch is closed, the ring will __________ .

Calculate magnetic flux density of the magnetic field at the centre of a circular coil of 50 turns, having a radius of 0.5m and carrying a current of 5 A.

Find magnetic flux density at a point on the axis of a long solenoid having 5000 tums/m when it carrying a current of 2 A.

Answer the following question.
When a conducting loop of resistance 10 Ω and area 10 cm2 is removed from an external magnetic field acting normally, the variation of induced current-I in the loop with time t is as shown in the figure.
Find the
(a) total charge passed through the loop.
(b) change in magnetic flux through the loop
(c) magnitude of the field applied

Magnetic flux is ______.

The magnetic flux linked with a coil of N turns of area of cross-section A held with its plane parallel to the field B is ______.

Two inductors of inductance L each are connected in series with the opposite? magnetic fluxes. The resultant inductance is ______.

The magnetic flux linked with a coil in Wb is given by the equation Φ = 3t2 + 4t + 9. Then the magnitude of induced emf at t = 2 sec will be ______.

The dimensions of magnetic flux are ______

The unit of magnetic flux in SI is ______

The dimensional formula of magnetic flux is ______.

A square of side L meters lies in the x-y plane in a region, where the magnetic field is given by `B = Bo(2hati + 3hatj + 4hatk)`T, where B0 is constant. The magnitude of flux passing through the square is ______.

A cylindrical bar magnet is rotated about its axis (Figure). A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be: (Assume the coil to be short circuited.)

A circular coil of 1000 turns each with area 1 m2 is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ______ V.

A circular coil has radius ‘r', number of turns ‘N’ and carries a current ‘I’. Magnetic flux density ‘B’ at its centre is ______.


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