4.1: Charges and Electric Fields

Learning Objectives

• Describe how positive and negative charges are influenced by electric fields.
• Predict how objects with different charge attract or repel each other.
• Determine Electric Force vectors from on charges in an Electric field.

Model

The set of parallel arrows that all point in the same direction represent a constant electric field in the direction of the arrows. The arrows attached to each charged circle represent the electric force that charge experiences from the electric field.

Explore

1. Which direction is the electric field?
2. Circle the charges that experience an upward force. What is true about all of them?
3. Box the objects that experience a downward force. What is true about all of them?
4. There should be one object left over. How is it different from the rest?

Critical Thinking & Concept Invention

1. Summarize the patterns you observed:
   • Positive (+) charges experience a force that is __________ the direction of the electric field.
   • Negative (−) charges experience a force that is __________ the direction of the electric field.
   • Objects with more charge experience __________ force.
   • Neutral objects ______________________________.

Summary

The electric force an object experiences is based on the charge (\(q\)) of an object and the strength and direction of the electric field (\(\vec{E}\)). This force is given by the vector equation:

\[\vec{F}_e=q\vec{E}\]

The negative sign that occurs when \(q\) is negative flips the direction of the force so that it opposes the direction of the electric field.

Model

Explore

1. Next to each pair, write Attracts or Repels based on the direction of the forces.
2. Fill in the table below to identify the number of charges in each pair and the strength of the attractive or repulsive force.

Critical Thinking & Concept Invention

1. Identify whether each of the following depends on the types of charge (+/−) or the amount of charge:
   • The direction of the electric force (attraction or repulsion) depends on __________________.
   • The magnitude of the electric force depends on __________________.
2. Create a rule: When do objects attract and when do they repel?
3. Create a rule: What determines the numerical magnitude of the electric force between two objects?

Apply

In each scenario below, the middle charge is fixed and cannot move.

1. Annotate the diagram with the following:
   • Next to each charge around the middle charge, write attract or repel to identify the direction of the force on that charge from the middle charge only.
   • Next to each outer charge, draw an arrow to identify the direction that the electric field must point to create a force that matches your selection of attraction or repulsion.

Model

Explore

1. Fill in the equation to determine the force that each charge experiences, then draw a force vector for each charge.
2. Is Charge 1 positive or negative? Is Charge 2 positive or negative?
   • Charge 1 is ______.
   • Charge 2 is ______.
3. How does the direction of the force compare to the direction of the electric field?
   • The force on Charge 1 points ______ the direction of the electric field.
   • The force on Charge 2 points ______ the direction of the electric field.

Critical Thinking & Concept Invention

1. How does the direction of the force on positive and negative charges compare to the direction of the electric field?
   • For positive charges: ______
   • For negative charges: ______
2. Explain mathematically why the direction differs for positive and negative charges.
3. If both charges were free to move, identify the direction each charge would accelerate and explain your reasoning.

Summary

The electromagnetic force on a charged object depends on its charge \(q\), the electric field \(\vec{E}\), its velocity \(\vec{v}\), and the magnetic field \(\vec{B}\):

\[ \vec{F}_e=q\left(\vec{E}+\vec{v}\times\vec{B}\right) \]

When the magnetic field is zero, this simplifies to:

\[ \vec{F}_e=q\vec{E} \]

A negative value of \(q\) reverses the direction of the force relative to the electric field.