Question

A particle of charge $q$ and mass $m$ is moving through a region of space at right angles to an electric field and a magnetic field, where the crossed magnetic and electric fields produce a zero net force on the charge. If the speed of the charge is doubled, which of the following changes will again produce a zero net force on the charge?

• A. Reducing the Electric field to $\frac{1}{2}E$
• B. Increasing the Electric field to $2E$
• C. Reducing the Magnetic field to $\frac{1}{2}B$
• D. Increasing the Magnetic field to $2B$
• E. Doubling both the Magnetic and Electric Fields

Answer 1

Answer: (B), (C)

The correct options are
B Increasing the Electric field to $2E$
C Reducing the Magnetic field to $\frac{1}{2}B$

Magnetic force on charge q , moving with velocity v , in a magnetic field of strength B at right angle is given by ,

$F_B=qvB$ ,

electric force on charge q in an electric field E , is given by ,

$F_E=qE$ ,

as the net force is zero , therefore magnetic force and electric force should be equal and opposite ,

$F_B=F_E$ ,

or $qvB=qE$ ,

or $v=E/B$ ...............................eq1 ,

now if velocity v is doubled , $=2v$ , to keep the right hand side of eq1 equal to v , we can increase electric field to $2E$ or decrease magnetic field to $B/2$ .