Asolid metal cylinder of radius a and length l, carrying charge λ per unit length, is surrounded by a thin metal cylinder with radius b and the same length. the outer cylinder carries no net charge. (a) find the charge densities per unit area at the inner and outer surfaces of the outer cylinder. (b) find the potential at the center, using radius b as the reference point. (c) how do your answers to (a) and (b) change when the outer surface is touched to a grounding wire? (e) find the electrostatic energy per unit length of the coaxial cylinders when the outer cylinder is charged by -a per unit length.

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Aturntable that spins at a constant 74.0 rpm takes 3.10 s to reach this angular speed after it is turned on. find its angular acceleration (in rad/s2), assuming it to be constant, and the number of degrees it turns through while speeding up.

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?