Advertisements
Advertisements
Question
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`
Advertisements
Solution
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
RELATED QUESTIONS
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.
Can a charged particle be accelerated by a magnetic field? Can its speed be increased?
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 rigid wire consists of a semi-circular portion of radius R and two straight sections (figure). The wire is partially immersed in a perpendicular magnetic field B, as shown in the figure. Find the magnetic force on the wire if it carries a current i.
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.
Figure shows a part of an electric circuit. The wires AB, CD and EF are long and have identical resistance. The separation between the neighbouring wires is 1.0 cm. The wires AE and BF have negligible resistance and the ammeter reads 30 A. Calculate the magnetic force per unit length of AB and CD.
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?
A charged particle is moving on circular path with velocity v in a uniform magnetic field B, if the velocity of the charged particle is doubled and strength of magnetic field is halved, then radius becomes ______.
A current of 3 A is flowing in a linear conductor having a length of 40 cm. The conductor is placed in a magnetic field of strength of 500 gauss and makes an angle of 30° with the direction of the field. It experiences a force of magnitude:
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:
A conducting loop of resistance R and radius r has its centre at the origin of the coordinate system in a magnetic field of induction B. When it is rotated about y-axis through 90°, the net charge flown in the loop is directly proportional to:
