Question

An electric field of $1500 V m^{-1}$ and a magnetic field of $0.04 Wb m^{-2}$ act on moving electrons. The minimum uniform speed along a straight line the electron could have is
a) $1.6 \times 10^{15} ms^{-1}$
b) $6 \times 10^{-16} ms^{-1}$
c) $3.75 \times 10^{4} ms^{-1}$
d) $3.75 \times 10^{2} ms^{-1}$

Answer 1

An electron is moving with speed (assume it v) under the influence of electric field and magnetic field. We have to find a uniform speed that means acceleration should be zero and by Newton's second law, force should be zero if acceleration is zero.

Complete answer:
Given, electric field, E = $1500 V m^{-1}$.
Magnetic field, B = $0.04 Wb m^{-2}$
Electric field and magnetic field acts on electrons cause electric force and magnetic force comes into play respectively.
Due to electric field, electric force is as follows –
$F=QE$
Due to magnetic field, magnetic force is as follows –
$F=vQB$
We need to find uniform speed; acceleration is equal to zero.
So, net force is equal to zero.
Therefore, electric force is equal to the magnetic force.
$QE =vQB$
$v = \dfrac{E}{B}$
$v = \dfrac{1500 V m^{-1}}{0.04 Wb m^{-2}}$
$v= 37500 m s^{-1}$
$3.75 \times 10^{4} ms^{-1}$

Option (c) is correct.

Additional Information:
Electric field and magnetic field are inter-linked in a field termed as an electromagnetic field. In that field, they move perpendicular to each other. Though, they are independent with each other. Without the electric field, the magnetic field persists in permanent magnets, and electric fields live in static electricity without magnetic field presence.

Note:
The important point in this question is we need uniform velocity. For uniform velocity, acceleration needs to be zero. If a particle having mass m and moving with zero acceleration i.e., no change in velocity. It means force needs to be zero on the particle.