Advertisements
Advertisements
Question
Consider a solid sphere of radius r and mass m that has a charge q distributed uniformly over its volume. The sphere is rotated about its diameter with an angular speed ω. Show that the magnetic moment µ and the angular momentum l of the sphere are related as `mu = q/(2m) l`
Advertisements
Solution
Considering the strip of width dx at a distance x from the centre of the sphere.
Small area of the strip is given as,
da = 4π x dx
`i = (dq)/(dt) = (qw)/(2pi)`
`mu= ia = (qw)/(2pi)4pi` \[\int\limits\] `x dx`
`= q.wr^2 = q/ml`
APPEARS IN
RELATED QUESTIONS
Which of the following particles will have minimum frequency of revolution when projected with the same velocity perpendicular to a magnetic field?
A particle moves in a region with a uniform magnetic field and a parallel, uniform electric field. At some instant, the velocity of the particle is perpendicular to the field direction. The path of the particle will be
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 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.
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`
Consider a straight piece of length x of a wire carrying a current i. Let P be a point on the perpendicular bisector of the piece, situated at a distance d from its middle point. Show that for d >> x, the magnetic field at P varies as 1/d2 whereas for d << x, it varies as 1/d.
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.
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).
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 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 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:
