Q. 305.0( 1 Vote )

A particle having a charge of 2.0 × 10–8 C and a mass of 2.0 ×10–10 g is projected with a speed of 2.0 × 103 ms–1 in a region having a uniform magnetic field of 0.10 T. The velocity is perpendicular to the field. Find the radius of the circle formed by the particle and also the time period.

Given-

Charge on the particle, q = 2.0 × 10−8 C

Mass of the particle, m = 2.0 × 10−10 g

velocity of the particle when projected, v = 2.0 × 103 m s−1

Magnetic field, B = 0.10 T.

Given in the question that, the velocity is perpendicular to the field.

So, for the particle to move in a circle, the centrifugal force comes into acts which is provided by the magnetic force acting on it.

Also magnetic force, we know, Lorentz force F is given by -

where,

e = charge on an electron

v = velocity of the electron

B=magnetic field

Using the formula for centrifugal force

where,

v= velocity of the particle

m =mass of the electron

Equating the two forces, we will get-

Now,

Time period,

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