<< Chapter < Page | Chapter >> Page > |
(a) An electron gun has parallel plates separated by 4.00 cm and gives electrons 25.0 keV of energy. What is the electric field strength between the plates? (b) What force would this field exert on a piece of plastic with a charge that gets between the plates?
Strategy
Since the voltage and plate separation are given, the electric field strength can be calculated directly from the expression . Once the electric field strength is known, the force on a charge is found using . Since the electric field is in only one direction, we can write this equation in terms of the magnitudes, .
Solution for (a)
The expression for the magnitude of the electric field between two uniform metal plates is
Since the electron is a single charge and is given 25.0 keV of energy, the potential difference must be 25.0 kV. Entering this value for and the plate separation of 0.0400 m, we obtain
Solution for (b)
The magnitude of the force on a charge in an electric field is obtained from the equation
Substituting known values gives
Discussion
Note that the units are newtons, since . The force on the charge is the same no matter where the charge is located between the plates. This is because the electric field is uniform between the plates.
In more general situations, regardless of whether the electric field is uniform, it points in the direction of decreasing potential, because the force on a positive charge is in the direction of and also in the direction of lower potential . Furthermore, the magnitude of equals the rate of decrease of with distance. The faster decreases over distance, the greater the electric field. In equation form, the general relationship between voltage and electric field is
where is the distance over which the change in potential, , takes place. The minus sign tells us that points in the direction of decreasing potential. The electric field is said to be the gradient (as in grade or slope) of the electric potential.
In equation form, the general relationship between voltage and electric field is
where is the distance over which the change in potential, , takes place. The minus sign tells us that points in the direction of decreasing potential. The electric field is said to be the gradient (as in grade or slope) of the electric potential.
For continually changing potentials, and become infinitesimals and differential calculus must be employed to determine the electric field.
Notification Switch
Would you like to follow the 'Physics 101' conversation and receive update notifications?