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.
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 __________ .
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 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 dimensions of magnetic flux are ______
The unit of magnetic flux in SI is ______
The dimensional formula of magnetic flux 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
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 ______.
A circular coil has radius ‘r', number of turns ‘N’ and carries a current ‘I’. Magnetic flux density ‘B’ at its centre is ______.
