An electron is moving on a circular path of radius r with speed v in a transverse magnetic field B, then \(\frac{e}{m}\) will be:

CONCEPT:

Lorentz force:

• 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

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⇒ FL = qE + qvBsinθ 

• A charged particle experiences a force when it moves in a magnetic field.
• The magnetic force is given as,

​
⇒ F = qvBsinθ

• 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:

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\(⇒ r=\frac{mv}{qB}\)

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:

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\(⇒ r=\frac{mv}{qB}\)     -----(1)

By equation 1,

\(⇒ r=\frac{mv}{eB}\)

\(⇒ \frac{e}{m}=\frac{v}{rB}\)

• Hence, option 3 is correct.