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>> $A charged particle with velocity vec v =$

Question

A charged particle with velocity $v = x \hat{i} + y \hat{j}$ moves in a magnetic field $B = y \hat{i} + x \hat{j}$ . The force acting on the particle has magnitude $F$ . Which one of the following statements is/are correct?

This question has multiple correct options

A

No force will act on charged particle if $x = y$

B

If $x > y, F \propto (x^{2} - y^{2})$

C

If $x > y$ , the force will act along z-axis

D

If $y > x$ , the force will act along y-axis

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Updated on : 2022-09-05

Solution

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Correct options are A) , B) and C)

$v = x \hat{i} + y \hat{j}$

$B = y \hat{i} + x \hat{j}$

$f = q (v \times B) = q ((x \hat{i} + y \hat{j}) \times (y \hat{i} + x \hat{j})) = q (x^{2} - y^{2}) \hat{k}$

If $x = y$ , $f = q (x^{2} - y^{2}) = q (0 - 0) = 0$

If $x > y$ , $f = q (x^{2} - y^{2}) \hat{k} > 0$

If $y > x$ , $f = q (x^{2} - y^{2}) \hat{k} < 0$ and it points in the $- v e z -$ axis.

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