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(a) Derive the expression for the torque...

(a) Derive the expression for the torque on a rectangular current carrying loop suspended in a uniform magnetic field.
(b) A proton and a deuteron having equal momenta enter in a region of uniform magnetic field at right angle to the direction of the field. Depict their trajectories in the field.

Text Solution

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(b) When a charged particle of charge .q. and momentum .p. enters in a region of uniform magnetic field `vecB` at right angle to the direction of the field, it describe a circular trajectory of radius
`r = p/(qB)`
As proton and deuteron have same charge and equal momenta, hence both will revolve in exactly the same circular path as shown fig.
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A proton and a deutron having equal momenta enter in a region of uniform magnetic field at right angles to the direction of the field. Depict their trajectories in the field.

(a)Derive the expression for the torque on a rectangular current carrying loop suspended in a uniform magnetic field. (b)A proton and a deuteron having equal momenta enter in a a region of a uniform magnetic field at right angle to the direction of a the field.Depict their trajectories in the field. OR (a)A small compass needle of magnetic moment m is free to turn about an axis perpendicular to the direction of unifrom magnetic field B .The moment of inertia of the needle about the axis is I .The needle is slightly disturbed form its stable position and then released.Prove that it executes simple harmonic motion.Hence deduce the expression for its time period. (b) A compass needle, free to turn in a vertical plane orients inself with its axis vertical at a certain place on the earth.Find out the values of (i)horizontal component of earth's magnetic field and (ii) angle of dip at the place.

Knowledge Check

  • A current carrying loop in a uniform magnetic field will experience

    A
    force only
    B
    torque only
    C
    both torque and force
    D
    neither torque nor force
  • A rectangular current carrying loop in a uniform magnetic field experiences___________

    A
    force
    B
    torque
    C
    both A and B
    D
    pressure
  • An electron and a proton with equal momentum enter perpendicularly into a uniform magnetic field, then

    A
    The path of proton shall be more curved than that of electron
    B
    The path of proton shall be less curved than that of electron
    C
    Both are equally curved
    D
    Path of both will be straight line
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