Physics Book - User contributions [en]

Electric Field and Electric Potential

2025-11-13T03:20:40Z

Mkane41:

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

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ELECTRIC POTENTIAL!
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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.

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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.

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EXAMPLES
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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.

Electric Field and Electric Potential

2025-11-13T03:19:49Z

Mkane41:

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.

Electric Field and Electric Potential

2025-11-03T14:54:22Z

Mkane41:

MEIRA KANE FALL 2025
Electric Field and Electric Potential

ELECTRIC FIELD:
What is it??
Electric fields and electric potentials describe how charges interact at a distance.
The electric field (
𝐸
⃗
E
) shows the direction and strength of force on a positive test charge, while electric potential (
𝑉
V) represents potential energy per unit charge at a point in space.

These two quantities are closely related:

Electric field is vector (has direction).

Electric potential is scalar (has magnitude only).

The field always points in the direction of decreasing potential.

Key Definitions

Electric Field:

𝐸
⃗
=
𝐹
⃗
𝑞
E
=
q
F

The force per unit charge. Units:
N/C
N/C.

Electric Potential Energy:

U=qV

The work needed to bring a charge
𝑞
q from infinity to that point.

Electric Potential:

Units:
J/C
J/C (also known as Volts).

Electric Field and Electric Potential

2025-11-03T14:50:24Z

Mkane41: Created page with "MEIRA KANE FALL 2025"

MEIRA KANE FALL 2025