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A particle having a charge of 10 muCand mass of 1mug moves in a horizontal circle of radius 10cm under the influence of magnetic field of 0.1T.when the particle is at a point P,a uniform electric field is switched on so that the particle starts moving along the tangent with uniform velocity .The electric field is?
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A particle having a charge of 10 muCand mass of 1mug moves in a horizo...
Given information:


  • Charge of the particle, q = 10 μC

  • Mass of the particle, m = 1 μg

  • Radius of the circular path, r = 10 cm

  • Magnetic field, B = 0.1 T



Calculating the velocity of the particle:


  • The magnetic force, F = qVB

  • Centripetal force, F = mv²/r

  • Equating the two forces, mv²/r = qVB

  • Velocity of the particle, v = √(qBr/m)

  • Substituting the given values, v = √(10*10^-6 * 0.1 * 0.1 / (1 * 10^-6)) = 1 cm/s



Calculating the electric field:


  • When the electric field is switched on, the particle moves along the tangent with uniform velocity.

  • Therefore, the electric force, Fe = qE, balances the magnetic force, Fm = qvB, in the horizontal direction.

  • qE = qvB

  • Electric field, E = vB = 1 cm/s * 0.1 T = 0.1 V/cm



Conclusion:


  • The electric field required to move the particle along the tangent with uniform velocity is 0.1 V/cm.

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A particle having a charge of 10 muCand mass of 1mug moves in a horizontal circle of radius 10cm under the influence of magnetic field of 0.1T.when the particle is at a point P,a uniform electric field is switched on so that the particle starts moving along the tangent with uniform velocity .The electric field is?
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