Question

An $\alpha $ particle of mass $6.65 \times {10^{ - 27}}kg$ travels at right angles to a magnetic field of 0.2T with a speed of $6 \times {10^5}m/s.$ The acceleration of a particle will be
A. $7.55 \times {10^{11}}m{s^{ - 2}}$
B. $5.77 \times {10^{11}}m{s^{ - 2}}$
C. $7.55 \times {10^{12}}m{s^{ - 2}}$
D. $5.77 \times {10^{12}}m{s^{ - 2}}$

Answer 1

Hint: In order to solve this question, we will first calculate the force on the alpha particle and then the acceleration of the particle can be calculated by using the newton's second law of motion i.e. by dividing the force with the mass of the alpha particle.

Formula used-
The magnetic force on a particle is given by ${F_b} = qVB$
Where
q is the charge on the alpha particle
V is the velocity of the alpha particle
B is the magnetic field

Complete step-by-step answer:
Given
$
  q = 2e = 2 \times 1.602 \times {10^{ - 19}}C \\
  v = 6 \times {10^5}m{s^{ - 1}} \\
  B = 0.2T \\
 $
 Now substitute these values in the above equation to find the force on the particle
$
  {F_b} = qVB \\
  {F_b} = 2 \times 1.602 \times {10^{ - 19}} \times 6 \times {10^5} \times 0.2 \\
  {F_b} = 384.48 \times {10^{ - 19}}N \\
 $
Now the acceleration of the particle can be calculated as
$a = \dfrac{{{F_b}}}{m}$
$m = 6.65 \times {10^{ - 27}}kg$
Substituting the value of force and mass in the above equation to calculate the acceleration
$a = \dfrac{{384.48 \times {{10}^{ - 19}}}}{{6.65 \times {{10}^{ - 27}}}} = 5.77 \times {10^{12}}m{s^{ - 2}}$
Hence, the acceleration of the body is $5.77 \times {10^{12}}m{s^{ - 2}}$ and the correct option is D.

Additional Information- Whenever a charged particle passes through a magnetic field it experiences force whether it positively charged or negatively, just having the opposite direction of force. Only condition is that it must be in motion at some angle with the magnetic field except the particle must not be parallel to the field.
In the case of a positive charge, the force on a charged particle due to an electric field is directed parallel to the electric field vector, and in the case of a negative charge, the force is directed antiparallel. It isn't dependent on particle velocity. By contrast, a charged particle's magnetic force is orthogonal to the magnetic field vector, and depends on the particle's velocity. You can use the right hand rule to determine the direction of the force.

Note: The magnetic field does not work, so a charged particle's kinetic energy and speed remains constant in a magnetic field. The magnetic force, acting perpendicular to the particle's velocity, will cause circular motion. Also when the charged particle velocity is parallel to the magnetic field then there is no force on the particle and the particle moves in a straight line.