Chapter 5, Problem 5.12P

Show if the potential changes in the following relation  V(r)  In this case, we only have a non-circular closed path when n = -2 .

Find the potential inside and outside a spherical shell of radius R that carries a uniform surface charge density of Sigma0. Set the reference point at infinity. Draw a graph of this potential as a function of r, the spherical radius.

The Brachistochrone Problem: Show that if the particle is projected withan initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloidpassing through the two points with a cusp at a height z above the initialpoint given by v02 = 2gz.

Consider two points in an electric field. The potential at P1 is V1= -30V and the potential at P2= 150. How much work does an external force do when moving a load q= -4.7 μC, from P1 to P2?

Find a scalar potential, fi, if  F=(3x^2yz^2)i+(x^3z^2)j+(2x^3yz)k, and fi(1,1,1)=1

An isolated solid spherical conductor of radius 5.00 cm is surrounded by dry air. It is given a charge and acquires potential V, with the potential at infinity assumed to be zero. (a) Calculate the maximum magnitude V can have. (b) Explain clearly and concisely why there is a maximum.

Consider a particle moving in the region x > 0 under the influence of the potential where U0 = 1 J and α = 2 m. Plot the potential, find the equilibrium points, and determine whether they are maxima or minima.

Can you Solve Q(7-8-9) please

A ring with radius R and a uniformly distributed total charge Q lies in the xy plane, centered at the origin. What is the potential V(z) due to the ring on the z axis as a function of z? What is the magnitude of the electric field E on the z axis as a function of z, for z>0?