Crossed electric and magnetic fields are established over a certain region. The magnetic field is 0.105 T and the electric field is 2.00 ｘ 10⁵ V/m. An electron, experiences zero net force from these fields and so continues moving in a straight line. What is the electron's speed? (Answer: 1.9x 10⁶ m/s) 



Given:


Magnetic Field = B = 0.105 T

Electric Field = E = 2.00 ｘ 10⁵ V/m

Net Force on Electron = F = 0 N


To Find:

Speed of the Electron = v = ?


Solution:

The formula for Lorentz Force formula acting on charge particle moving in the region of both electric and magnetic field

→F→F = q ( →E→E + →v→v  ｘ →B→B  ) 

As →F→F = 0 N, So

→E→E + →v→v  ｘ →B→B  = 0

or

→E→E = - →v→v  ｘ →B→B 

→v→v  and →B→B are at right angle so sinθ = 1 

now taking absolute values

|→E→E| = E = v B

or

v = EBEB


by putting the corresponding values

v = 2.00ｘ10⁵Vm0.105T

v = 19.048 ｘ 10⁵ m/s

or

v = 1.9 ｘ 10⁶ m s⁻¹ ------------------ Ans.



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