Question

A particle having a charge of 10 uC and mass 1 ug moves in a horizontal
radius 10 cm under the influence of a magnetic field of 0.1 T. When the party
at a point P, a uniform electric field is switched on so that the particle starts
along the tangent with uniform velocity. The electric field is
(1) 01 Vim
(2) 1.0 V/m
(3) 10.0 V/m
(4) 100 V/m​

Answer 1

The value of electric field is E = 10 N/C

Explanation:

Given data:

Charge on particle "q" = 10μC = 10 × 10^-6 C = 10^-5 C

Mass of particle "m" = 1μg = 10^-9 kg

Magnetic field , B = 0.1 T

Magnetic force "F" = q(v × B) = qvBsinθ

= 10^-5 × v × 0.1 T × sin90°

= 10^-6 × v .....(1)

• Radius of circle, r = mv/qB

v = qBr/m ......(2)

• Now comparing equations (1) and (2).

F = 10^-6 × {10^-5 C × 0.1 T × 0.1 m/10^-9 kg}

= 10^-4 N

• Force due to electric field "F" = qE 10^-4 = 10^-5 × E  E = 10 N/C

Thus the value of electric field is E = 10 N/C

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