Question

A Positive charge 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 is F. Which one of the following statements are correct :

• A. no force will act on particle of x = y
• B. $F\propto (x^2-y^2)$ if x > y
• C. the force will act along positive Z-axis if x > y
• D. the force will act along positive Z-axis if y > x

Answer 1

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

The correct options are
A no force will act on particle of x = y
B $F\propto (x^2-y^2)$ if x > y
C the force will act along positive Z-axis if x > y

The magnetic force on a particle moving with velocity 'v' in a given magnetic field is given by
$\overrightarrow{F}=\overrightarrow{v}\times \overrightarrow{B}$
$\overrightarrow{F}=(xi+yj)\times (yi+xj)$
$\overrightarrow{F}=x^{2}k+y^2(-k)$
$\overrightarrow{F}=x^{2}k-y^{2}k$
If $x=y,F=(x^2-y^2)k=0$
$F>0$ if $x>y$. So the force acts in positive z- direction if x > y