Question

Electron of mass m and charge q is travelling with a speed v along a circular path of radius r at right angles to a uniform magnetic field of intensity B. If the speed of the electron is doubled and the magnetic field is halved the resulting path would have a radius.

• A. $2r$
• B. $4r$
• C. $r/4$
• D. $r/2$

Answer 1

The correct option is B $4r$

Given,

Mass of electron=m

Charge of electron=q

Velocity of electron=V

Radius of electron = r

Magnetic field =B

We know that force due to magnetic field, $F_B=qvB$

Now if $V^{{}^{\prime }}=2V\text{and}{B}^{{}^{\prime }}=\frac{B}{2}$

Then $F_B^{{}^{\prime }}=q{V}^{{}^{\prime }}{B}^{{}^{\prime }}=q\left(2V\right)\left(\frac{B}{2}\right)$

$F_B=\frac{m{V}^2}{r}$

$⟹r=\frac{m{V}^2}{qVB}⟹r=\frac{mV}{qB}$ and

$r^{{}^{\prime }}=\frac{m\left(2V\right)}{q\left(\frac{B}{2}\right)}$

$r^{{}^{\prime }}=4r$