Electric Potential and Energy: Problems & Solutions
Electric Potential Energy Change: Electron in Thunderstorm
During a thunderstorm, the electric potential difference between a cloud and the ground is Vcloud – Vground = 1.3 x 108 V, with the cloud being at the higher potential. What is the change in an electron’s electric potential energy when the electron moves from the ground to the cloud?
Work Done by Electric Force on a Sodium Ion
Suppose that the electric potential outside a living cell is higher than that inside the cell by 0.070 V. How much work is done by the electric force when a sodium ion (charge = +e) moves from the outside to the inside?
Translational Speed of a Charged Particle
A negatively charged particle is released from rest at point B and accelerates until it reaches point A. The mass and charge of the particle are 4.0 x 10-6 kg and -2.0 x 10-5 C, respectively. Only the gravitational force and the electrostatic force act on the particle, which moves on a horizontal straight line without rotating. The electric potential at A is 36 V greater than that at B; in other words, VA – VB = 36 V. What is the translational speed of the particle at point A?
Lightning Flash: Work, Speed, and Heat
During a lightning flash, there exists a potential difference of Vcloud – Vground = 1.2 x 109V between a cloud and the ground. As a result, a charge of -25 C is transferred from the ground to the cloud.
- How much work Wground→cloud is done on the charge by the electric force?
- If the work done by the electric force were used to accelerate a 1100-kg automobile from rest, what would be its final speed?
- If the work done by the electric force were converted into heat, how many kilograms of water at 0 °C could be heated to 100 °C?
Total Potential at a Point Due to Point Charges
The drawing shows four point charges. The value of q is 2.0 μC, and the distance d is 0.96 m. Find the total potential at the location P. Assume that the potential of a point charge is zero at infinity.
Particle Motion Near a Fixed Charge
A charge of -3.00 μC is fixed in place. From a horizontal distance of 0.0450 m, a particle of mass 7.20 x 10-3 kg and charge -8.00 μC is fired with an initial speed of 65.0 m/s directly toward the fixed charge. How far does the particle travel before its speed is zero?
The charge moves a distance 0.045m – 0.0108m = 0.0342m
Distance Between Equipotential Surfaces
Two equipotential surfaces surround a +1.50 x 10-8 C point charge. How far is the 190-V surface from the 75.0-V surface?
Electric Field in a Cell Membrane
The inner and outer surfaces of a cell membrane carry a negative and a positive charge, respectively. Because of these charges, a potential difference of about 0.070 V exists across the membrane. The thickness of the cell membrane is 8.0 x 10-9 m. What is the magnitude of the electric field in the membrane?
Potential Difference Across a Spark Plug
A spark plug in an automobile engine consists of two metal conductors that are separated by a distance of 0.75 mm. When an electric spark jumps between them, the magnitude of the electric field is 4.7 x 107 V/m. What is the magnitude of the potential difference ΔV between the conductors?
Potential in a Constant Electric Field
An electric field has a constant value of 4.0 x 103 V/m and is directed downward. The field is the same everywhere. The potential at a point P within this region is 155 V. Find the potential at the following points:
- 6.0 x 10-3 m directly above P
- 3.0 x 10-3 m directly below P
- 8.0 x 10-3 m directly to the right of P
Potential Difference of a Capacitor
What is the potential difference between the plates of a 3.3-F capacitor that stores sufficient energy to operate a 75-W light bulb for one minute?
Dielectric Constants of Capacitors with Different Plate Shapes
Two capacitors have the same plate separation, but one has square plates and the other has circular plates. The square plates are a length L on each side, and the diameter of the circular plate is L. The capacitors have the same capacitance because they contain different dielectric materials. The dielectric constant of the material between the square plates has a value of κsquare = 3.00. What is the dielectric constant κcircle of the material between the circular plates?
