A particle with positive charge q = 2.72 10-18 C moves with a velocity v with arrow = (5î + 4ĵ − k) m/s through a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total force on the moving particle, taking B with arrow = (3î + 3ĵ + k) T and E with arrow = (2î − ĵ − 5k) V/m.

Explanation:

The charge, q, of the particle is

The velocity, v, of the particle is (5i + 4j - k) m/s

It moves in a region containing electric field, E, of (2i - j - 5k) V/m and magnetic field, B, of (3i + 3j + k) T.

The electric force acting on the particle is given as:

where v X B is cross product.

Therefore:

Let us solve (5i + 4j - k) X (3i + 3j + k):

i(4 + 3) - j(5 + 3) + k(15 - 12) = 7i - 8j + 3k

Therefore: