Download How do We Make a Uniform Electric Field?

Charges in a Uniform Electric Field
Flashback
Remember:
𝐸=
𝐹
𝑘𝑄
= 2
𝑞
𝑟
What is a Uniform Electric Field?
This is an area of space where the electric field is the same.
How do We Make a Uniform Electric Field?
We take two metal plates and hook them up to a battery. The battery takes electrons from the
positive sides and pushes them onto the negative side. We end up with one plate having a
negative charge and the other having an equal negative charge. That means that between the
plates we have a steady uniform electric field.
Work inside a Uniform Electric Field
Let’s imagine we put a positive charge into an electric field.
High Potential
Low Potential
The difference in potential between the two plates is equal to the voltage of the battery charging them.
If you follow field lines, the electric potential decreases.
If we want to find the work an electric field does in moving a charge from one plate to another, we would have to use
some equations we’ve learned through the course of this unit.
𝑊 = 𝐹𝑑
𝑊𝑓𝑖𝑒𝑙𝑑 = −∆𝑈
𝑊 = 𝑞𝐸𝐷
𝑊 = −∆𝑈 = −𝑞∆𝑉
If we put these together we get:
Memorize This!
Memorize This!
𝑉 = 𝐸𝑑
∆𝑉𝑞 = ∆𝑈
Where V is the voltage of the battery, E is the electric field between the plate and d is the distance between the plates
Practice Problem: Field Between Plates
You hook a 300V battery up to two metal plates and put them a distance 0.6 cm apart.
a) What is the strength of electric field between the plates?
b) A proton is between these two plates. A proton has a mass of 1.67 x 10-27 kg. What will the acceleration of the
proton be as it moves between these two plates?
c) How fast is the proton moving when it hits the opposite plate? ? Assume it starts from rest at the positive
plate.
AP Practice Problem: Parallel Plate Free Response Problem
2002B5B (Modified). Two parallel conducting plates, each of area 0.30 m2, are separated by a distance of 2.0 × 10 –2 m
of air. One plate has charge +Q; the other has charge –Q. An electric field of 5000 N/C is directed to
the left in the space between the plates, as shown in the diagram above.
a. Indicate on the diagram which plate is positive (+) and which is negative (–).
b. Determine the potential difference between the plates.
An electron is initially located at a point midway between the plates.
d. Determine the magnitude of the electrostatic force on the electron at this location and state its
direction.
e. If the electron is released from rest at this location midway between the plates, determine its speed just
before striking one of the plates. Assume that gravitational effects are negligible.
Shooting a Particle Between Two Parallel Plates
Most AP problems don’t just have us watching a particle accelerate from rest. Instead, they like to have us shoot the
particle in between the two plates.
Is the particle that followed this path
positively or negatively charged?
It might not look like it, but this is basically a horizontal projectile problem.
Walking through the Variables
Imagine two electrons are being shot through two oppositely parallel plates. I will walk you through how to set this
problem up in class.
AP Practice Problem: Two Charged Plates
1985B3. An electron initially moves in a horizontal direction and has a kinetic energy of 2.0 × 103 electron–volts when it is
in the position shown above. It passes through a uniform electric field
between two oppositely charged horizontal plates (region I) and a field–free region (region II) before
eventually striking a screen at a distance of 0.08 meter from the edge of the plates. The plates are 0.04
meter long and are separated from each other by a distance of 0.02 meter. The potential difference
across the plates is 250 volts. Gravity is negligible.
a. Calculate the initial speed of the electron as it enters region I.
b. Calculate the magnitude of the electric field E between the plates, and indicate its direction on the diagram above.
c. Calculate the magnitude of the electric force F acting on the electron while it is in region I.
d. On the diagram below, sketch the path of the electron in regions I and II. For each region describe the
shape of the path.