# Electric Potential Practice Problems

Two hollow plastic globes of radius 4.50 cm and 8.40 cm are concentric with each other. The globe of radius 4.50cm has a charge of -12.5 nC distributed evenly on its surface. Similarly, the other globe has a charge of +8.25 nC evenly distributed over its surface. If the electric potential is zero at an infinitely large distance, determine the resultant electric potential from the two globes at i) r = 0 cm ii) r = 6.00 cm iii) r = 8.40 cm.

An experimental setup consists of two charged particles K = +1.20 µC and L = -3.60 µC. Their separation is 29.0 cm. Assuming the electric potential is zero at infinity, determine the electric potential at a point that is 20.0 cm from K and 21.0 cm from L.

During an experiment, charged particles M and N are placed 65.0 cm apart. Their charges are M = -8.50 µC and N = +3.50 µC. If the electric potential is zero at infinity, determine the electric potential at a point between the two charges, 30.0 cm from charge M.

Two charged particles with a separation x have the same kind of charge and equal magnitude. Considering an axis joining the two particles, determine all points on the axis where the electric field is zero. Will the electric potential be zero at the points you identified?

Two charged particles carry the same kind of change and the same magnitude. Their separation is x. For an axis passing through both particles, determine all points where the electric potential is zero (Take the electric potential to be zero at infinity). Will the electric field be zero at the points you have identified?

A rectangle measures 0.0400 m by 0.0500 m. Particles of charges +4.00 nC and -4.00 nC are placed on two adjacent corners separated by the shorter length. What is the electric potential at the center of the rectangle due to the two charges? Take potential to be zero at infinity.

Two particles charged to +3.80 μC and +5.50 μC are fixed in place 0.400 m apart. A proton is dropped at rest at the midpoint of the two charges. If the proton moves purely along the line joining the two charged particles, determine its speed when at a distance of 18.0 cm from the +3.80 μC particle.

A test charge carries a charge of -7.20 μC and has a mass of 0.240 g. It is moved from point P to point Q. The potential at P and Q is +125 V and 584 V respectively. If the net force on the test charge is the electric force and the charge has a speed of 2.40 m/s at point P, calculate its speed at point Q.

A very long horizontal wire has a uniform linear charge density of 92.0 µC/m. A radioactive nuclide emits an alpha particle (mass = 6.64 × 10^{-27} kg, charge = +2e) toward the wire. Its speed is 1.4 × 10^{7} m/s when at a position 28.0 cm from the wire. What is the kinetic energy of the alpha particle?

A charged particle lies at the origin of a xy plane. The electric field magnitude at point p from the origin is 27.4 V/m while the electric potential is 14.1 V. What is the direction of the electric field at point p? Take the electric potential to be zero at infinity.

Students place a charged particle at point a. They find the electric field magnitude to be 84.6 V/m while the potential is 50.0 V at point b. Determine the magnitude of the charge on the particle if the potential is zero at infinity.

The electric potential at point p from a charged particle is 10.2 V. The electric field at that same point has a magnitude of 22.5 V/m. Calculate the length from the charge to point p. Assume potential is zero at infinity.

During an experiment, a group of students placed a negatively charged particle -q at x,y = 0,-2. A second negatively charged -Q particle is placed at x,y = -2,0. Make a sketch showing the locations of the charges.

A proton has a speed 3.5 × 10^{6} m/s. The speed of the proton should be increased to 7.5 × 10^{6} m/s. Determine the potential difference along the proton's path that will achieve this increase.

Two equal and large metallic sheets are charged with opposite charges to the same magnitude. The separation of the sheets is 54 mm. Determine the magnitude of the electric field between the two plates given that the surface charge density on each sheet is 20.2 nC/m^{2}.

Two equal giant sheets of metal are placed parallel to each other with a separation of 54 mm. The sheets are charged by induction, charging them with opposites charges to a charge density of magnitude 20.2 nC/m^{2}. The separation of the sheets is tripled while the charge density is kept the same. Determine the change in the electric field and the potential difference between the plates.

a) A steel ball has a radius of 20.0 cm. The electric potential of the ball's center relative to infinity is 1.2 kV. Determine the value of the unbalanced charge on the ball. b) Determine the potential at the surface of the ball relative to infinity.

Consider two point charges: one carrying a negative charge of -2.0 nC and the other carrying a positive charge of +5.0 nC. Assume the positive charge is located at x = 0 cm, and the negative charge is at x = 2.0 cm on the x-axis. At what point or points on the x-axis does the electric potential become zero?

Consider a positively charged sphere in space with a radius of 0.5 mm. Two points are measured from the centre of the sphere, one at 3.0 mm and another at 6.0 mm. A voltage difference of 400 V exists between these two points. Determine the sphere's charge.

Using the expression for electric potential at a point P located at a perpendicular distance R from a thin wire of length L with a uniform linear charge density λ as shown below, determine the electric field E at point P.