Problems on the electric potential
1- A proton is released from rest in a uniform electric field that has a magnitude of 8.0x104 V/m
along the +ve x-axis. The proton undergoes a displacement of 0.5 m in the direc"on of E
a. Find the change in electric potential between points A and B
b. Find the change in potential energy of the proton for this displacement
c. Find the speed of the proton at point B
2- An electron moving parallel to the x-axis has an ini"al speed of 3.7x106 m/s at the origin. Its
speed is reduced to 1.4x105 m/s at the point x=2 cm. Calculate the poten"al difference between
the origin and this point.
3- Find the potential at point P. Find the change in potential energy of 3µC charge as it moves from
infinity to point P. What is the total potential of the system.
4- Over a certain region of space, the electric poten"al is V=5x-3x2y+2yz2. Find the electric field
over this region, and what is the magnitude of E at (1,0,-2) m?
5- An electric field is given by E=2xi+3y2j. Find (VA-VB) between the points rA=i-2j to rB=2i+j+3k
6- A rod of length L lies along the x axis with its left end at the origin. It has a nonuniform
charge density λ = αx, where α is a positive constant. (a) What are the units of α? (b)
Calculate the electric potential at A and point B.
7- A wire having a uniform linear charge density λ is bent into the shape shown. Find the
electrical potential at point O.
8- Calculate the electric potential at point P on the axis of the annulus shown which has a
uniform charge density σ.
9- Two conduc"ng spheres with diameters of 0.4 m and 1.0 m are separated by a distance that is
large compared with the diameters. The spheres are connected by a this wire and charged to
7µC.
a. How is the total charge shared between the spheres
b. What is the potential of the system
10- The potential in a region between x = 0 and x = 6.00 m is V = a + bx, where a = 10.0 V and b
= –7.00 V/m. Determine (a) the potential at x = 0, 3.00 m, and 6.00 m, and (b) the
magnitude and direction of the electric field at x = 0, 3.00 m, and 6.00 m.