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What uniform magnetic field, applied perpendicular to a beam of electrons moving at 1.30×106 m/s, is required to make the electrons travel in a circular arc of radius 0.350 m?

Short Answer

Expert verified

The required magnetic field is2.11×10-5T .

Step by step solution

01

Listing the given quantities

  • Velocity isV = .1.3×106″¾/²õ
  • Radius is r =.0.350 m
02

Understanding the concept of centripetal force and magnetic field

Weuse the equilibrium condition of the magnetic force on the electron and centripetal force due to the circular path.

Formula:

Fm=qvB

Fc=mv2r

03

 Step 3: Explanation

For the circular motion of an electron:

Fm=FcqvB=mv2rB=mvrq

Substituting the given values in the above expression, and we get,

B=9.11×10-31×1.3×1060.35×1.6×10-19=2.11×10-5 T

The required magnetic field is2.11×10-5 T .

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