Question

A charged particle with velocity $\overrightarrow{v}=x\hat{i}+y\hat{j}$ moves in a magnetic field $\overrightarrow{B}=y\hat{i}+x\hat{j}$. The magnitude of magnetic force acting on the particles F. Among the following the correct statement(s) is/are :

• A. no force will act on particle, if $x=y$
• B. $F\alpha (x^2-y^2)$ is x > y
• C. the force will act along z-axis, if x > y
• D. the force will act along y-axis, if y > x

Answer 1

Answer: (A), (B), (C)

The correct options are
A no force will act on particle, if $x=y$
B $F\alpha (x^2-y^2)$ is x > y
C the force will act along z-axis, if x > y

$F=q\left(vXB\right)$

$vXB=(xi+yj)X(yi+xj)=(x^2-y^2)k$

$F\propto (x^2-y^2)k$ is $x>y$

NO force will act if $x=y$ $F=0$.

The force will directed in z direction.as $F=q(x^2-y^2)k$