A particle of charge q moves with velocity\(\vec { v } \) along positive y-direction in a magnetic field \(\vec { B } \) .Compute the Lorentz force experienced by the particle
(a) when magnetic field is along positive y - direction
(b) when magnetic field points in positive z - direction
(c) when magnetic field is in zy - plane and making an angle θ with velocity of the particle. Mark the direction of magnetic force in each case

An electron moving perpendicular to a uniform magnetic field 0.500 T undergoes circular motion of radius 2.50 mm. What is the speed of electron?

Two singly ionized isotopes of uranium \(_{ 92 }^{ 235 }{ U \ and \ _{ 92 }^{ 238 }{ U } }\) (isotopes have same atomic number but different mass number) are sent with velocity 1.00 x 10⁵ m s^–1 into a magnetic field of strength 0.500 T normally. Compute the distance between the two isotopes after they complete a semi-circle. Also, compute the time taken by each isotope to complete one semi-circular path. (Given: masses of the isotopes: m₂₃₅ = 3.90 x 10^–25 kg and m₂₃₈ = 3.95 x 10^–25 kg)

Suppose a cyclotron is operated to accelerate protons with a magnetic field of strength 1 T. Calculate the frequency in which the electric field between two Dees could be reversed.

Consider a circular wire loop of radius R, mass m kept at rest on a rough surface. Let I be the current flowing through the loop and  be the magnetic field acting along horizontal as shown in Figure. Estimate the current I that should be applied so that one edge of the loop is lifted off the surface?