JEE Advanced Physics

A capacitor has rectangular plates of length a and width b. The top plate is inclined at a small angle as shown. The plate separation varies d = y0 at the left to d = 2y0 at the right, were y0 is much less than a or b. calculate the capacitance of the system?

Let the x - y plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has refractive index of √2 and medium 2 with z < 0 has a refractive index of √3. A ray of light in medium 1 given by the vector A = 6√3i + 8√3j - 10k in incident on the plane of separation. The angle of refraction in medium 2 is
a. 75°
b. 60°
c. 45°
d. 30°

Two metal strips, each of length l are clamped parallel to each other on a horizontal floor with a separation b between them. A wire of mass m lies on them perpendicularly a s shown in the figure. A vertically upward magnetic field of strength B exists in the space. The metal strips are smooth but the coefficient of friction between the wire and the floor is u. A current i is established when the switch S is closed at the instant t=0. Discuss the motion of the wire after the switch is closed. How far away from the strips will the wire reach?