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
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.
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
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.
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.
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 ______.
The magnetic flux linked with the coil (in Weber) is given by the equation- Փ = 5t2 + 3t + 16. The induced EMF in the coil at time, t = 4 will be ______.
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 ______
A loop, made of straight edges has six corners at A(0, 0, 0), B(L, O, 0) C(L, L, 0), D(0, L, 0) E(0, L, L) and F(0, 0, L). A magnetic field `B = B_o(hati + hatk)`T is present in the region. The flux passing through the loop ABCDEFA (in that order) 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.
In a coil of resistance 100 Ω a current is induced by changing the magnetic flux through it. The variation of current with time is shown in the figure. The magnitude of change in flux through the coil 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'?
