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Question

A proton moving with a velocity of (6^i+8^j)×105 ms1 enters uniform magnetic field of induction 5×103^kT . The magnitude of the force acting on the proton is :
(^i,^j and ^k are unit vectors forming a right handed triad)

A
0
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B
8×1016N
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C
3×1016N
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D
4×1016N
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Solution

The correct option is B 8×1016N
Force on a charged particle in magnetic field is given by,
¯F=q(V×B)
=1.6×1019((6^i+8^j)×5^k)×105×103
=1.6×1019×102(30^j+40^i)
=1.6×1016(3^j+4^i)
|F|=1.6×101632+42
=1.6×1016×5N
=8×1016N

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