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>>Moving Charges and Magnetism
>>Lorentz Force
>> $A charged particle moves with velocity v$

Question

A charged particle moves with velocity $v = a \hat{i} + d \hat{j}$ in a magnetic field $B = A \hat{i} + D \hat{j}$ . The force acting on the particle has magnitude $F$ . Then,

A

$F = 0$ , if $a D = d A$

B

$F = 0$ , if $a D = - d A$

C

$F = 0$ , if $a A = - d D$

D

$F \propto (a^{2} + b^{2})^{1 / 2} \times (A^{2} + D^{2})^{1 / 2}$

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Updated on : 2022-09-05

Solution

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Correct option is A)

$F = q (v \times B)$

$= q ((a \hat{i} + d \hat{j}) \times (A \hat{i} + D \hat{j}))$

$= q (a D - d A) \hat{k}$

If $a D - d A = 0$

$F = 0$

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