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1. Write the expression for the force, $\overrightarrow{\text{F}}$, acting on a charged particle of charge 'q', moving with a velocity$\overrightarrow{\text{v}}$ in the presence of both electric field $\overrightarrow{\text{E}}$and magnetic field $\overrightarrow{\text{B}}.$ Obtain the condition under which the particle moves undeflected through the fields.
2. A rectangular loop of size l x b carrying a steady current I is placed in a uniform magnetic field $\overrightarrow{\text{B}}.$ Prove that the torque$\overrightarrow{\tau}$ acting on the loop is given by $\overrightarrow{\tau} =\overrightarrow{\text{m}}\times\overrightarrow{\text{B},}$were $\overrightarrow{\text{m}}$is the magnetic moment of the loop.