Advertisements
Advertisements
Question
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 ______.
Options
`2 B_0 L^2 Wb`
`3 B_0 L^2 Wb`
`4 B_0 L^2 Wb`
`sqrt(29) B_0 L^2 Wb`
Advertisements
Solution
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 `underline(4 B_0 L^2 Wb`).
Explanation:
Magnetic flux is defined as the total number of magnetic lines of force passing normally through an area placed in a magnetic field and is equal to the magnetic flux linked with that area.
For elementary area dA of a surface flux linked `dphi = BdA cos theta` or `dphi = vecB*dvecA`
So, Net flux through the surface `phi = oint vecB xx dvecA = BA cos theta`
In this problem, `A = L^2 hatk` and `B = B_0 (2hati + 3hatj + 4hatk)T`
`phi - vecB.vecA = B_0 (2hati + 3hatj + 4hatk) * L^2 hatk = 4B_0L^2 Wb`
APPEARS IN
RELATED QUESTIONS
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.
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 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?
Figure shows a rectangular loop conducting PQRS in which the arm PQ is free to move. A uniform magnetic field acts in the direction perpendicular to the plane of the loop. Arm PQ is moved with a velocity v towards the arm Rs. Assuming that the arms QR, RS and SP have negligible resistances and the moving arm PQ has the resistance r, obtain the expression for (i) the current in the loop (ii) the force and (iii) the power required to move the arm PQ.
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
Whenever the magnetic flux linked with an electric circuit changes, an emf is induced in the circuit. This is called ______.
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 unit of magnetic flux in SI is ______
The dimensional formula of magnetic flux is ______.
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 ______.
The Figure below shows an infinitely long metallic wire YY' which is carrying a current I'.
P is a point at a perpendicular distance r from it.
- What is the direction of magnetic flux density B of the magnetic field at the point P?
- What is the magnitude of magnetic flux density B of the magnetic field at the point P?
- Another metallic wire MN having length l and carrying a current I is now kept at point P. If the two wires are in vacuum and parallel to each other, how much force acts on the wire MN due to the current I' flowing in the wire YY'?
