Electric Potential Energy Practice Problems

A point charge q = -2.80 μC has a fixed position. A tiny ball of mass 8.00 g is charged Q = -6.20 μC and shot toward the point charge. When the ball is 75 cm from the point charge, its speed is 17.0 m/s. What is the speed of the ball when it is 35 cm from the point charge? Treat the ball as a point charge and ignore weight. 

In an attempt to merge two hydrogen ions into a single atom, the separation of the ions is changed slowly from 1.1 × 10^-11 m to 2.0 × 10^-15 m. a) Calculate the work done in changing the separation. b) The ions slip from rest and start moving away from each other. What's their speed when the separation is 1.1 × 10^-11 m?

There are two point charges on the y-axis. One has a charge of -3.0 μC and is located 4.0 cm above the origin. The other has a charge of +5.0 μC and is located 7.0 cm above the origin. A third point charge with charge +4.0 μC is placed on the x-axis at a distance of 6.0 cm in the positive direction of the x-axis from the origin. What is the potential energy of this group of charges?

There are two charged particles on the x-axis. One has a charge of -5.0 nC and is located 2.0 cm to the right of the origin. The other has a charge of +10.0 nC and is located 5.0 cm to the right of the origin. What is the electric potential energy of the two charged particles?

Two point charges are on the x-axis: +2.0 μC at 4.0 cm and -3.0 μC at 8.0 cm from the origin. Place a third charge on the y-axis 6.0 cm from the origin. Find the value of this charge to make the total electric potential energy of the system zero.

Two parallel metal plates are separated by a distance of 5.0 mm and have a potential difference of 100 V applied across them. A charged particle with a charge of +2.0 μC and mass of 1.25 x 10^-13 kg is released from rest at the positive plate. What is the velocity of the particle just before it hits the negative plate?

In the proximity of a uniformly charged sphere, the electric potential at point S is determined to be 60 V. Moving 3.0 μm away from point S to point T; the potential has decreased by 0.24 mV. Determine the distance between point S and the center of the sphere.

Calculate the potential difference between two points on the y-axis at -3 cm and 4 cm if you're at a science museum where a uniform electric field is demonstrated with a strength of Ē = (10,000î-40,000ĵ) V/m. 

Sarah has a small sphere with a charge of -4.0 nC, and Alex has another small sphere with a charge of +5.0 nC. Sarah's sphere is at y= -8.0 cm, while Alex's sphere is at y=14.0 cm on the y-axis. On the x-axis, at what points does the electric potential become zero?

A flat, infinitely large plane with a surface charge density of -2.9×10⁻⁶ C/m² attracts an alpha particle propelled away from it at an initial velocity of 1.6×10⁶ m/s. How far does the particle travel before being drawn back toward the plane?

Four point charges are arranged as shown in the figure. Determine the electric potential energy of the arrangement.

Consider two negative point charges separated by a distance of 8.00 cm. Determine the magnitude of the electric force between the two charges if the electric potential energy is 120 μJ.

Suppose two point particles with charges, Q_a = 6.0 μC and Q_b = 5.0 μC, are initially fixed 5.0 cm apart. The masses of the particles are m_a = 3.0 mg and m_b = 4.0 mg. Determine the speed of Q_a after it is released from rest and moves infinitely far away from Q_b while Q_b remains fixed at its initial position.

Determine the ratio of the speeds of a proton that starts from rest and acquires 3.5 keV of kinetic energy when moving from point X to point Y.

Suppose two point charges, one with a charge of +8 μC and a mass of 4 mg, and the other with a charge of +8 μC and a mass of 6 mg, are kept at a distance of exactly 6 cm apart from each other. If both of these point charges were to be released simultaneously from the at rest state, what would be the velocity attained by the first charge after an infinite amount of time has passed? Disregard any external factors.

A metallic sphere with a radius of 5.0 cm carries an electric charge of 10 μC uniformly distributed over its surface. What is the total electrostatic potential energy of this sphere?

On an unknown planet, there is an electric field of about 180 V/m directed upwards from its surface. Two similar metal spheres having mass 'm' equal to 0.75 kg are released from a height 'h' of 2.5 m above the surface. One of the spheres is negatively charged with q₁ equal to -300 μC, while the other sphere is positively charged with q₂ equal to +300 μC. Determine the difference in their velocities when they touch ground using principles of conservation of mechanical energy. Assume that the gravitational acceleration on the planet is 3.7 m/s².

A proton at rest is initially positioned 25.0 cm away from a stationary point charge with charge Q = 0.085 nC. The charge Q is fixed in its position. Determine the speed of the proton when it moves far from the point charge due to electric repulsion. [Hint: The charge of a proton is 1.602 × 10^-19 C and its mass is 1.67 × 10^-27 kg.]

One stationary point charge is kept at a distance of 0.15 m from another similar charge located in space. They both have a charge of -4 μC and a mass of 0.50 mg. Given that they both start moving simultaneously due to electric repulsion, determine their speed when they reach an infinite separation.

A new type of sneakers advertises that the maximum static electricity generated by each individual sneaker would be 4.5 kV. Assuming that the sneakers and the ground are sheets of charge having a separation distance of s = 1.2 mm, estimate the magnitude of maximum charge transferred between each sneaker and the ground. [Hint: A typical human foot has dimensions of 25 cm × 10 cm.]

An alpha particle is initially moving at a speed of 1,100,000 m/s. Find the potential difference needed to bring the alpha particle to rest.