Question

A uniform electric field $E$ in the $y$ direction and uniform magnetic field $B$ in $x$ direction exists in free space. A particle of mass $m$ and carrying charge $q$ is projected from the origin with speed $v_0$ along the $x-$axis. The speed of particle as a function of $y$ co-ordinate will be

• A. $\sqrt{V_0^2+2qEy/m}$
• B. $\sqrt{V_0^2+qEy/m}$
• C. $\sqrt{V_0^2-2qEy/m}$
• D. $V_0+\sqrt{2qEy/m}$

Answer 1

The correct option is C $\sqrt{V_0^2-2qEy/m}$

A uniform electric field $E$ in $y$ direction uniform magnetic field $B$ $P_n$ $x$ direction.

Particle of mass $=m$

carrying charge $=q$

speed $=V_0$ (along $X-$axis)

Now, using the law of kinetic we get,

$\frac{1}{2}{mV}_0^2=qEy$

or, $V_y^2=\frac{2q{E}_y}{m}$

or, $V_y=\sqrt{\frac{2q{E}_y}{m}}$

Now,

The resultant will be $R=\sqrt{V_0^2-V_y^2}=\sqrt{V_0^2-\frac{2q{E}_y}{m}}$