Author Jonathan David
Author Jonathan David
Lessons

21. Electric Charge and Electric Field

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This Crash Course Outline is Based on The University Physics with Modern Physics Textbook

Young, Hugh D., Roger A. Freedman, Todd R. Sandin, and A. Lewis Ford. University Physics with Modern Physics. 15th ed. Pearson, 2019.

[21.3] Excess Electrons on a Charged Sphere: Finding the Count- This video calculates the number of

Excess electrons are placed on a small lead sphere with a mass of 8.00 g so that its net charge is -3.20 × 10⁻⁹ C. (a) Find the number of excess electrons on the sphere.

Electric Charge and Electric Field

Electric Charge and Electric Field

Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force in an electric field. There are two types of charges:

  • Positive Charge: Found on particles like protons.
  • Negative Charge: Found on particles like electrons.

Charges interact with each other through the principle of attraction and repulsion:

  • Like charges repel each other.
  • Opposite charges attract each other.

The unit of charge is the coulomb (C). The elementary charge is denoted as e:

    \[e = 1.6 \times 10^{-19} \, \text{C}\]

Electric Field

An electric field is a region around a charged particle where other charges experience a force. The field is represented by field lines:

  • Field lines point away from positive charges and toward negative charges.
  • The density of the lines indicates the strength of the field.

The electric field \vec{E} at a point is defined as the force \vec{F} experienced by a small positive test charge q divided by the magnitude of the charge:

    \[\vec{E} = \frac{\vec{F}}{q}\]

The unit of the electric field is \text{N/C} (newtons per coulomb).

Coulomb’s Law

Coulomb’s law describes the force between two point charges. The magnitude of the force F is given by:

    \[F = k_e \frac{|q_1 q_2|}{r^2}\]

Here:

  • F: The electric force between the charges.
  • k_e = 8.99 \times 10^9 \, \text{N·m}^2/\text{C}^2: Coulomb’s constant.
  • q_1 and q_2: The magnitudes of the charges.
  • r: The distance between the charges.

Electric Field Due to a Point Charge

The electric field produced by a point charge Q at a distance r is given by:

    \[E = k_e \frac{|Q|}{r^2}\]

The direction of the field depends on the sign of the charge:

  • For a positive charge, the field radiates outward.
  • For a negative charge, the field points inward.

Superposition Principle

When multiple charges are present, the total electric field at a point is the vector sum of the fields due to each charge. Mathematically:

    \[\vec{E}_{\text{total}} = \sum \vec{E}_i\]

Key Takeaways

Electric charge is the foundation of electrostatics, and the electric field describes how charges influence the space around them. Coulomb’s law and the concept of superposition provide tools for calculating forces and fields in complex systems.

[21.4] Electric Field and Electric Forces: A uniform electric field exists in the region between …

A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cm distant from the first, in a time interval of 3.20 × 10⁻⁶ s.

[21.5] Electric-Field Calculations: A uniform line of charge with length 20.0 cm is along the x-axis

A uniform line of charge with length 20.0 cm is along the x-axis, with its midpoint at x = 0. Its charge per length is +4.80 nC/m. A small sphere with charge -2.00 μC is located at x = 0, y = 5.00 cm. What are the magnitude and direction of the force that the charged sphere exerts on the line of charge?

[21.7] Electric Dipoles: Point charges q1 = -4.5 nC and q2 = +4.5 nC are separated by 3.1 mm, …

Point charges q1 = -4.5 nC and q2 = +4.5 nC are separated by 3.1 mm, forming an electric dipole. [a] Find the electric dipole moment (magnitude and direction). [b] The charges are in a uniform electric field whose direction makes an angle of 36.9° with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude 7.2 × 10⁻⁹ N·m?