Question

A charged particle moves with velocity $\vec{v}=a \hat{i}+d \hat{j}$ in a magnetic field $\vec{B}=A \hat{i}+D \hat{j}$. 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. $F \propto\left(a^{2}+b^{2}\right)^{1 / 2} \times\left(A^{2}+D^{2}\right)^{1 / 2}$

Answer 1

Answer: (A)

$\vec{F} \propto(\vec{v} \times \vec{B})=\hat{k}[a D-d A]$
If $F=0, a D=d A$