Question

A particle having the same charge as an electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5T. If an electric field of 100 V/m makes it move in a straight path, then the mass of the particle is ………...?
(Given charge of electron = $1.6\times {{10}^{-19}}C$)
$\begin{aligned} & \left( a \right)\text{ }2.0\times {{10}^{-24}}kg \\\ & \left( b \right)\text{ }1.6\times {{10}^{-19}}kg \\\ & \left( c \right)\text{ }1.6\times {{10}^{-27}}kg \\\ & \left( d \right)\text{ }9.1\times {{10}^{-31}}kg \\\ \end{aligned}$

Answer 1

Hint: To solve this question both the concept of magnetic and the electric field is used that means this question involves both the units (electrostatic and magnetism). Equate magnetic force and centrifugal force and solve further.

Complete step by step answer:
To solve this question, we focus on the two things. First the electric field (a field that surrounds the electric charge and put the attraction or the repulsion force on other electric charges) and the magnetic field (a field that explains the electric charges magnetism impact their relative motion). We will use both the formula to get our answer. The mathematical expression can be written as –
When the particle is moving under influence of magnetic field will be,
$\begin{aligned} & \dfrac{m{{v}^{2}}}{R}=qvB \\\ & \Rightarrow mv=qBR..........(1) \\\ \end{aligned}$
When particle is moving in straight line, we get
$\begin{aligned} & qE=qvB \\\ & \Rightarrow v=\dfrac{E}{B}..............(2) \\\ \end{aligned}$
Substituting value from equation (2) in equation (1), we get
$m=\dfrac{q{{B}^{2}}R}{E}$
Substituting the given values, we get
$\begin{aligned} & \Rightarrow m=\dfrac{1.6\times {{10}^{-19}}\times {{\left( 0.5 \right)}^{2}}\times 0.5\times {{10}^{-2}}}{100} \\\ & \Rightarrow m=2.0\times {{10}^{-24}}kg \\\ \end{aligned}$
Hence the mass of the particle is $2.0\times {{10}^{-24}}kg$.
So, the correct option is (a).

Additional information:
In the above question we have to find the mass of the particle so first we get a brief description of a mass. Mass is a characteristic of any physical matter (matter is the one that has mass). Mass is called the actual weight of anybody yet mass and weight are the two different phenomena. Mass is fixed of any object. The two objects of the same mass can have a different weight as the weights can get affected due to gravitational force.

Note: Always note the values given in questions carefully and by using relevant formulas calculate them nicely because even a small value can affect your result and may turn it wrong. Remember when a particle is moving in a magnetic field then the particle experiences magnetic force, and if the particle is moving in circular path then it experiences centrifugal force also. And these two forces, that is magnetic force and centrifugal force are the same. Students often forget to equate this and make mistakes.