Question

If a particle of charge \[{10^{ - 12}}C\] moves along the \[X\]-axis with a velocity \[{10^5}m/s\]. experiences a force of \[{10^{ - 10}}N\] in y-direction due to magnetic field, then the minimum magnetic field is
A. \[6.25 \times {10^3}T\] in \[Z\] direction
B. \[{10^{ - 15}}T\] in \[Z\] direction
C. \[6.25 \times {10^{ - 3}}T\] in \[Z\] direction
D. \[{10^{ - 3}}T\]in \[Z\] direction

Answer 1

Hint: In the given question, we need to determine the minimum magnetic field. For this, we need to use the formula for force experienced by a charged particle in an external magnetic field to get the desired result.



Formula used:
The following formula is used for solving the given question.
Magnetic force experienced by a charged particle is \[F = qvB\sin \theta \].
Here, \[F\] is the force, \[B\] is the magnetic field, \[q\] is the charge of a particle, \[v\] is the velocity and \[\theta \] is the angle between velocity and magnetic field.



Complete answer:
We know that the magnetic force experienced by a charged particle is \[\vec F = q(\vec v \times \vec B)\].
Here, \[F\] is the force, \[B\] is the magnetic field, \[q\] is the charge of a particle and \[v\] is the velocity.
So, consider the following figure for this.

Image: Direction of cross product of magnetic field and velocity
We can define it as \[F = qvB\sin \theta \]
Here, we can say that \[B\] will be minimum only when \[\theta = {90^o}\].
So, we get \[B = \dfrac{F}{{qv}}\]
But \[F = {10^{ - 10}}N\] , \[q = {10^{ - 12}}C\] and \[v = {10^5}m/s\]
Thus, \[B = \dfrac{{{{10}^{ - 10}}}}{{{{10}^{ - 12}} \times {{10}^5}}}\]
By simplifying, we get
\[B = {10^{ - 3}}T\] in \[Z\] direction.
Hence, the minimum magnetic field is \[{10^{ - 3}}T\] in \[Z\] direction.

Therefore, the correct option is (D).


Note: We can say that a charged particle moving in a magnetic field feels a force from the magnetic field. Thus, the Lorentz force is the name given to this force. Many students make mistakes in the calculation part as well as in determining the value of \[\theta \]. So, it is essential to write a proper formula of magnetic force experienced by a charged particle and its diagrammatic representation to get the desired result.