Advertisements
Advertisements
प्रश्न
Consider a non-conducting plate of radius r and mass m that has a charge q distributed uniformly over it. The plate is rotated about its axis with an angular speed ω. Show that the magnetic moment µ and the angular momentum l of the plate are related as `mu = q/(2 m)l`
उत्तर
Given:
Radius of the ring = r
Mass of the ring = m
Total charge of the ring = q
Angular speed, w = `(2pi)/T ⇒ T = (2pi)/w`
Current in the ring, `i = q/t = (qw)/(2pi)`
For the ring of area A with current i, magnetic moment,
`mu = niA =ia [n = 1]`
= `(qw)/(2pi)xx pir^2 = (qwr^2)/(2)`
Angular momentum, `l = Iw`,
where I is the moment of inertia of the ring about its axis of rotation.
`I = mr^2`
`so, l =mr^2w`
⇒ `wr^2 = 1/m=`
Putting this value in equation (i), we get:
`mu = (ql)/(2m)`
APPEARS IN
संबंधित प्रश्न
Sketch the change in flux, emf and force when a conducting rod PQ of resistance R and length l moves freely to and fro between A and C with speed v on a rectangular conductor placed in uniform magnetic field as shown in the figure
A small compass needle of magnetic moment ‘m’ is free to turn about an axis perpendicular to the direction of uniform magnetic field ‘B’. The moment of inertia of the needle about the axis is ‘I’. The needle is slightly disturbed from its stable position and then released. Prove that it executes simple harmonic motion. Hence deduce the expression for its time period.
A short bar magnet of magnetic moment 0.9 J/T is placed with its axis at 30° to a uniform magnetic field. It experiences a torque of 0.063 J.
(i) Calculate the magnitude of the magnetic field.
(ii) In which orientation will the bar magnet be in stable equilibrium in the magnetic field?
You are facing a circular wire carrying an electric current. The current is clockwise as seen by you. Is the field at the centre coming towards you or going away from you?
A vertical wire carries a current in upward direction. An electron beam sent horizontally towards the wire will be deflected
A wire of length l carries a current i long the x-axis. A magnetic field exists, which is given as `vecB = B_0 (veci + vecj + veck)` T. Find the magnitude of the magnetic force acting on the wire.
A current of 5.0 A exists in the circuit shown in the figure. The wire PQ has a length of 50 cm and the magnetic field in which it is immersed has a magnitude of 0.20 T. Find the magnetic force acting on the wire PQ.
A long wire carrying a current i is bent to form a place along α . Find the magnetic field B at a point on the bisector of this angle situated at a distance x from the vertex.
A long, straight wire is fixed horizontally and carries a current of 50.0 A. A second wire having linear mass density 1.0 × 10−4 kg m−1 is placed parallel to and directly above this wire at a separation of 5.0 mm. What current should this second wire carry such that the magnetic repulsion can balance its weight?
Consider the situation shown in the figure. Suppose the circular loop lies in a vertical plane. The rod has a mass m. The rod and the loop have negligible resistances but the wire connecting O and C has a resistance R. The rod is made to rotate with a uniform angular velocity ω in the clockwise direction by applying a force at the midpoint of OA in a direction perpendicular to it. Find the magnitude of this force when the rod makes an angle θ with the vertical.
In the circuit shown in the figure, find the value of the current shown in the ammeter A.
Two infinitely long current carrying conductors X and Y are kept parallel to each other, 24 cm apart in a vacuum. They carry currents of 5A and 7A respectively, in the same direction, as shown in the figure below. Find the position of a neutral point, i.e., a point where resultant magnetic flux density is zero. (Ignore earth’s magnetic field).
A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires.
(a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?
(b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before?
(Ignore the mass of the wires) g = 9.8 m s–2.
Correct expression for force on a current carrying conductor of length dl in a magnetic field is ______.
An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true?
When a magnetic compass needle is carried nearby to a straight wire carrying current, then
- the straight wire cause a noticeable deflection in the compass needle.
- the alignment of the needle is tangential to an imaginary circle with straight wire as its centre and has a plane perpendicular to the wire.
A small object with charge q and weight mg is attached to one end of a string of length ‘L’ attached to a stationary support. The system is placed in a uniform horizontal electric field ‘E’, as shown in the accompanying figure. In the presence of the field, the string makes a constant angle θ with the vertical. The sign and magnitude of q ______.
A conducting ring of radius 1m kept in a uniform magnetic field B of 0.01 T, rotates uniformly with an angular velocity 100 rad s−1 with its axis of rotation perpendicular to B. The maximum induced emf in it is:
