Correct Answer - Option 3 :
\(\frac{v}{Br}\)
CONCEPT:
Lorentz force:
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It is defined as the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force on the charged particle is called the Lorentz force and is given by
⇒ FL = qE + qvBsinθ
- A charged particle experiences a force when it moves in a magnetic field.
- The magnetic force is given as,
⇒ F = qvBsinθ
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When the velocity of a charged particle is perpendicular to a magnetic field, it describes a circular path, and the radius of the circular path is given by:
\(⇒ r=\frac{mv}{qB}\)
Where, F = force due to magnetic field, m = mass, q = magnitude of charge, v = speed of charge, E = electric field, B = magnetic field and θ = angle between v and B
CALCULATION:
Given m = mass of the electron, q = e (charge on the electron), radius = r, speed = v, and magnetic field = B
- When the velocity of a charged particle is perpendicular to a magnetic field, it describes a circle and the radius of the circle is given by:
\(⇒ r=\frac{mv}{qB}\) -----(1)
By equation 1,
\(⇒ r=\frac{mv}{eB}\)
\(⇒ \frac{e}{m}=\frac{v}{rB}\)
- Hence, option 3 is correct.
