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Question: A particle with 10<sup>–11</sup> coulomb of charge and 10<sup>–7</sup> kg mass is moving with a velo...

A particle with 10–11 coulomb of charge and 10–7 kg mass is moving with a velocity of 108 m/s along the y-axis. A uniform static magnetic field B = 0.5 Tesla is acting along the x-direction. The force on the particle is

A

5 × 10–11 N along i^\hat { i }

B

5 × 103 N along k^\hat { k }

C

5 × 10–11 N along−j^- \hat { j }

D

5 × 10–4 N along −k^- \hat { k }

Answer

5 × 10–4 N along −k^- \hat { k }

Explanation

Solution

By using F⃗=q(v⃗×B⃗)\vec { F } = q ( \vec { v } \times \vec { B } ); where v⃗=10j^\vec { v } = 10 \hat { j } and B⃗=0.5i^\vec { B } = 0.5 \hat { i }

⇒\Rightarrow F⃗=10−11(108j^×0.5i^)=5×10−4(j^×i^)\vec { F } = 10 ^ { - 11 } \left( 10 ^ { 8 } \hat { j } \times 0.5 \hat { i } \right) = 5 \times 10 ^ { - 4 } ( \hat { j } \times \hat { i } ) =5×10−4(−k^)= 5 \times 10 ^ { - 4 } ( - \hat { k } ) i.e., 5×10−45 \times 10 ^ { - 4 }N along −k^- \hat { k }