Find the value of E such that a 750-eV electron moving in the negative x direction is undeflected

Question

A velocity selector consists of electric and magnetic fields described by the expression vectorE=Ek and vector B=Bj, with B=15.0 mT. Find the value of E such that a 750-eV electron moving in the negative x direction is undeflected. 

Answer 1

If the electron moves without being deflected, the electric and magnetic forces cancel.

 

F_E = -eE k

 

F_B = -e(-v i x B j) = evB k     (i x j = k)

 

 

F_E = F_B

 

-eE = evB

 

E = -vB = -√(2T/m)B     with T = ½mv²

 

E = -√(2*750*1.602x10^-19/9.11x10^-31) 15.0 x 10^-3 = -2.43 x 10⁵ N/m