Consider a line of charge that extends along the x-axis from x = -1.3 m to x = +1.3 m.  The line of charge has a nonlinear charge density given by ?λ(x) = 7.7 |x|  (nC/m).  (Note: that is the absolute value of x.)  Calculate the electric potential on the y-axis at y = 4.2 m, in V.  Use k = 9 x 109 N m2 / C2.  (Hint: Calculate the potential of the right half of the charge distribution and multiply by 2.)

The charge density on a disk of radius R = 13.0 cm is given by a = ar, with a = 1.44 µC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 34.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. V R A

The rectangle in the figure is 3 sidescapped by 5.0cm and 15cm, etq1 = −5μCetq2 = + 2.0μC. IfV = 0 at infinity, what is the electric potential (a) at corner A? (b) at corner B? (c) How much work does it take to move a third load q3 = +3.0 μC from point B to point A on the diagnonal of the rectangle? (d) Does this work increase or decrease the potential electrical energy of the three-load system? Is it greater than, less than or equivalent to the work required to move q3 on trajectories that are inside the rectangle but not on the diagnostic? (f) outside the rectangle? Please show formulas, thank you

Consider a ring of charge in the x-y plane of radius 2.7 m, centered at the origin.  The charge per angle around the ring is given by dQ/dα = a (1 - cos α)  (nC/rad), where a = 8.4 nC/rad.  Calculate the electric potential along the z axis at z = 5.8 m, in V.  Use k = 9 x 109 N m2 / C2. (Please answer to the fourth decimal place - i.e 14.3225)