Electric Field and Electric Potential
MEIRA KANE FALL 2025 Electric Field and Electric Potential
1. What is an electric field?
An electric field describes how charges influence the space around them. When a positive test charge is placed in an electric field, it experiences a force. The electric field tells us both the direction of this force and how strong the force is.
The electric field is defined as:
E = F / q
where: • E is the electric field • F is the electric force on a test charge • q is the magnitude of the test charge
This definition means the electric field tells us the force **per unit charge**.
2. Direction of the electric field
Electric field direction is always defined using a **positive test charge**: • Field points **away from positive charges** • Field points **toward negative charges**
Examples: • A single positive charge creates field lines pointing outward in all directions. • A single negative charge creates field lines pointing inward from all directions.
3. Properties of electric field lines
Electric field lines help visualize the field: • Lines start on positive charges and end on negative charges. • The density (spacing) of the lines shows field strength.
– Closer lines = STRONGER electric field – Spread-out lines = WEAKER electric field
• Electric field lines never cross. • The direction of the line gives the direction of the force on a positive charge.
4. Units of electric field
The electric field has units: • Newtons per Coulomb (N/C), because E = F / q or equivalently • Volts per meter (V/m), because of the relationship between field and potential.
5. How electric fields are created
Electric fields arise from: • Point charges • Continuous charge distributions • Conductors and insulators • Changing electric potential • Gauss’s Law situations with symmetric charge distributions
ELECTRIC POTENTIAL!
1. What is electric potential?
Electric potential (also called voltage) describes the **potential energy per unit charge** at a point in space. It is a **scalar** quantity, meaning it has magnitude but no direction.
Electric potential is defined as:
V = U / q
where: • V is electric potential • U is electric potential energy • q is charge
If a charge has high electric potential energy at a certain point, that point has high electric potential.
2. Units of electric potential
Electric potential is measured in **Volts (V)**, where: 1 Volt = 1 Joule / Coulomb
3. Reference point for potential
Electric potential is always measured relative to a reference. Common choices: • V = 0 at infinity (used for point charges) • V = 0 at the surface of a conductor • V = 0 at the ground or another convenient point
4. Changes in electric potential
A charge moving in an electric field undergoes changes in potential energy. Moving "with" the electric field decreases potential; moving "against" the electric field increases potential.
RELATIONSHIP BETWEEN ELECTRIC FIELD AND ELECTRIC POTENTIAL!
1. How they are connected
Electric field and electric potential are closely related. The electric field tells us how quickly the potential changes as we move through space.
In simple one-dimensional situations (movement along the x-axis):
E_x = - (change in potential) / (change in position)
This means: • Electric field points in the direction where electric potential decreases most rapidly. • E points from high potential to low potential.
2. Intuitive explanation
Imagine electric potential as "height" in a landscape and positive charges as balls on that landscape. • Electric potential = height • Electric field = slope
A ball always rolls downhill. Similarly, a positive charge always moves toward lower electric potential.
3. Important consequences
• Strong electric field → potential changes rapidly over a short distance. • Weak electric field → potential changes slowly. • If the electric field is zero in a region, the electric potential is constant in that region.
EXAMPLES
1. Example: Point charge
For a positive charge Q: • Electric field points outward. • Electric potential is highest near the charge and decreases as you move away.
2. Example: Uniform electric field
If the electric field is constant (same magnitude and direction everywhere): • Field lines are equally spaced and parallel. • Electric potential decreases linearly in the direction of the field.
3. Example: Parallel-plate capacitor
Between two charged parallel plates: • Electric field is nearly uniform. • Electric potential changes steadily from one plate to the other. • The positive plate has higher potential; negative plate has lower potential.