A particle of charge q moves with a velocity V = ai in a magnetic field B = b j + ck , where ' a ', ' b ' and ' c ' are constants. The magnitude of force experienced by particle is

Step-by-step solution

The magnetic force on a charged particle is given by the Lorentz force law: F = q ( V B ) . Given V = a i and B = b j + c k , the cross product is computed as: V B = (a i ) (b j + c k ) = ab( i j ) + ac( i k ) . Using the identities i j = k and i k = - j , the result simplifies to: V B = ab k - ac j . Substituting back into the force equation yields: F = q(ab k - ac j ) = -qac j + qab k . The magnitude is found using the Euclidean norm: | F | = (-qac)^2 + (qab)^2 = q^2 a^2 c^2 + q^2 a^2 b^2 = |qa| b^2 + c^2 . For p