Two parallel planes of current density k1 = -ky and k, = ky are located at z =ta. a. (5 pts.) find the force (magnitude and direction) on the current plane at z=ta by elementary methods. b. (10 pts.) repeat a using the stress tensor and show that you get the same answer.

Aperson stands on a platform, initially at rest, that can rotate freely without friction. the moment of inertia of the person plus the platform is ip. the person holds a spinning bicycle wheel with its axis horizontal. the wheel has moment of inertia iw and angular velocity ωw. take the ωw direction counterclockwise when viewed from above. part a what will be the angular velocity ωp of the platform if the person moves the axis of the wheel so that it points vertically upward?

In order of decreasing light-transmitting capabilities of materials, which is the correct sequence? a. transparent -> translucent -> opaque b. opaque -> transparent -> translucent c. opaque -> translucent -> transparent d. translucent -> transparent -> opaque

Estimate the schwarzschild radius (in kilometers) for a mini-black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (assume that the your weight is 50 kg)