Question

A particle of mass 0.6 g and having charge of 25 nC is moving horizontally with a uniform velocity ${1.2×10^4}$ ${ms^{-1}}$ in a uniform magnetic field, then the value of the magnetic induction is (g=10 ${ms^{-2}}$)
A . 0
B . 10 T
C . 20 T
D . 200 T

Answer 1

Hint: In this question we have to use the concept of uniform velocity, which will only be achieved if there is no acceleration of the object. We know that a charged particle experiences magnetic force in a magnetic field. But if the particle has no acceleration it means that it has no effective force working on it.



Formula used:
Magnetic force on the particle:
${F_m}$=qvB; here, q denotes the charge, v is the velocity of the particle, and B the magnetic field.
Gravitational force on the particle:
${F_g}$=mg: here, m denotes the mass of the particle and g is the acceleration due to gravity.


Complete answer:
For the particle to move with a uniform speed the two forces acting on it must cancel each other out. Which means the gravitational force and the magnetic force must be equal and acting in opposite directions.

Therefore, gravitational force=magnetic force
mg=qvB
$B=\dfrac{mg}{qv}$
$B=\dfrac{0.0006\times 10}{(25\times {{10}^{-9}})(1.2\times {{10}^{4}})}$
$B=20T$

The correct answer is C.

Note:Considering that a force is a vector quantity, it has both a magnitude (size) and a direction. There is no net force exerted on an object and it is considered to be in equilibrium if the amount and direction of the forces acting on it are precisely balanced. A particle will move with uniform velocity if there is no force acting on it, and the net acceleration will also be zero.