Question

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A proton moves through a region containing a uniform electric field given by E 41.0 j V/m and a uniform magnetic field B (0.200i0.300 j 0.400 R) T. Determine the acceleration of the proton when it has a velocity v231 î m/s. Need Help? Read It

Answer 1

Given,

E = 41 j V/m ; B = 0.2 i + 3 j + 4 k T ; v = 231 i m/s

We know that the electric and magnetic field acting at the same time exert a force given by

F = q (E + v x B)

F = 1.6 x 10^-19 [41 i + (231 i) x (0.2 i + 0.3 j + 0.4 k)]

(231 i) x (0.2 i + 0.3 j + 0.4 k)] = i (0 - 0) - j(231 * 0.4 - 0) + k(231 * 0.3 - 0) = 0i - 92.4 j + 69.3 k

F = 1.6 x 10^-19 [41 j + (0i -92.4 j + 69.3 k)]

F = 1.6 x 10^-19 (-51.4 j + 69.3 k )

Also, F = ma => a = F/m

a = 1.6 x 10^-19 (-51.4 j + 69.3 k )/1.67 x 10^-27 = 9.58 x 10^7 (-51.4 j + 69.3 k)

a = 9.58 x 10^7 (-51.4 j + 69.3 k) = -4.92 x 10^9 j + 6.64 x 10^9 k

Hence, a = (-4.92 x 10^9 j + 6.64 x 10^9 k) m/s^2