(a) Write the expression for the Lorentz force on a particle of charge $$q$$ moving with a velocity $$\vec{v}$$ in a magnetic field $$\vec{B}$$. When is the magnitude of this force maximum? Show that no work is done by this force on the particle during its motion from a point $$\vec{r_1} \text { to point } \vec{r}_2 \text {. }$$

OR

(b) A long straight wire $$A B$$ carries a current I. A particle (mass $$m$$ and charge $$q$$ ) moves with a velocity $$\vec{v}$$, parallel to the wire, at a distance $$d$$ from it as shown in the figure. Obtain the expression for the force experienced by the particle and mention its directions.

The potential difference applied across a given conductor is doubled. How will this affect (i) the mobility of electrons and (ii) the current density in the conductor? Justify your answers.

Two coils $$C_1$$ and $$C_2$$ are placed close to each other. The magnetic flux $$\phi_2$$ linked with the coil $$\mathrm{C}_2$$ varies with the current $$I_1$$ flowing in coil $$C_1$$, as shown in the figure. Find

(i) the mutual inductance of the arrangement, and

(ii) the rate of change of current $$\left(\frac{d \mathrm{I}_1}{d t}\right)$$ that will induce an emf of 100 V in coil C$$_2$$.

(a) A plane wave-front propagating in a medium of refractive index '$$\mu_1$$' is incident on a plane surface making an angle of incidence (i). It enters into a medium of refractive index $$\mu_2\left(\mu_2>\mu_1\right)$$. Use Huygen's construction of secondary wavelets to trace the retracted wave-front. Hence, verify Snell's law of refraction.

OR

Using Huygen's construction, show how a plane wave is reflected from a surface. Hence, verify the law of reflection.