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

`\vec F` = q ( `\vec E` + `\vec v`  ｘ `\vec B`  ) 

As `\vec F` = 0 N, So

`\vec E` + `\vec v`  ｘ `\vec B`  = 0

or

`\vec E` = - `\vec v`  ｘ `\vec B` 

`\vec v`  and `\vec B` are at right angle so sinθ = 1 

now taking absolute values

|`\vec E`| = E = v B

or

v = `\frac {E}{B}`


by putting the corresponding values

v = `\frac {2.00 ｘ 10⁵ V/m}{0.105 T}`

v = 19.048 ｘ 10⁵ m/s

or

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



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