Tru Physics

Electric Field

—

by

Tru Physics
in

The electric field is a concept which describes the influence that a charged object exerts on other charged objects around it. More specifically, it is a vector field that determines the force experienced by a charged particle when placed in its vicinity.

Basic Concepts of Electric Field

The electric field is a vector field that represents the effect of charged objects on the surrounding space. It is defined as the force (F) per unit of electric charge (q) experienced by a small test charge placed at a specific point in space. Mathematically, the electric field (E) can be expressed as:

E = \dfrac{F}{q}

The unit of the electric field is newtons per coulomb (N/C) or volts per meter (V/m). These two units are totally equivalent such that 1 \frac{N}{C} = 1 \frac{V}{m}. The direction of the electric field is the same as the direction of the force that a positive test charge would experience at that point.

Calculating the Electric Field

Electric Field of a Point Charge:

The electric field produced by a single point charge (Q) can be determined using Coulomb’s law. The electric field at a distance (r) from the point charge is given by:

|\vec{E}| = k \dfrac{|Q|}{r^2}

where k is the electrostatic constant (k \approx 8.99 \times 10^9 \frac{N \cdot m^2}{C^2}) and r is the distance from the charge. The electric field points radially outward from a positive charge and radially inward toward a negative charge.

Electric Field of a Uniformly Charged Insulating Sphere

For the uniformly charged, insulating sphere, the electric field can be calculated as if the sphere were simply a point charge such that:

|\vec{E}| = k \dfrac{|Q|}{r^2}.

Electric Field of an “Infinite” Plane Sheet of Uniform Charge Density

For an “infinite” plane of uniform area charge density (\sigma), the electric charge can be calculated by the formula:

|\vec{E}| = \dfrac{\sigma}{2 \varepsilon_0}

where \varepsilon_0 is the vacuum permittivity (\varepsilon_0 \approx 8.854 \times 10^{-12} F/m).

Note that \sigma can be calculated as:

\sigma = \dfrac{Q}{A} = \dfrac{[C]}{[m^2]}

Electric Field of an “Infinite” Uniform Line Charge

The electric field for an “infinite” line charge with uniform linear charge density \lambda can be written as:

|\vec{E}| = \dfrac{1}{2 \pi \varepsilon_0} \cdot \dfrac{\lambda}{r}

where r is the distance from the line of charge.

Note that \lambda can be calculated as:

\lambda = \dfrac{Q}{\ell}=\dfrac{[C]}{[m]}

Electric Field Between Two Parallel Conducting Plates

For two parallel conducting plates, the electric field

  1. Outside of the plates and at the plates is simply:

|\vec{E}|=0

  1. Bewteen the plates:

|\vec{E}|=\dfrac{\sigma}{\varepsilon_0}

Superposition Principle

The superposition principle states that the net electric field at a point in space due to multiple charges is the vector sum of the individual electric fields produced by each charge. This principle simplifies the analysis of complex systems of charges, as the electric field can be calculated independently for each charge and then combined to find the total field.

Electric Field Lines

Electric field lines are a visual representation of the electric field, showing the direction and relative strength of the field at various points in space. Field lines are drawn such that the tangent to the line at any point indicates the direction of the electric field at that point. The density of the field lines is proportional to the field’s strength. Some important properties of electric field lines are:

  1. Field lines always begin on positive charges and end on negative charges.
  2. Field lines never cross each other.
  3. The number of field lines emerging from or converging toward a charge is proportional to the magnitude of the charge.

Applications of Electric Fields

The study of electric fields and their associated phenomena has led to numerous practical applications in various fields, such as:

  1. Electrostatics: Understanding electric fields allows us to control and mitigate the effects of static electricity, which can cause damage to sensitive electronic components or create sparks that may ignite flammable materials.
  2. Electronics: Electric fields play a crucial role in the operation of electronic devices, such as transistors, capacitors, and other circuit components.
  3. Sensors: Electric field sensors are used in various applications, including non-contact voltage detection, touchscreens, and proximity sensing.
  4. Medical applications: Electric fields are employed in medical applications like electrotherapy, electroencephalography (EEG), and transcranial magnetic stimulation (TMS).

Want to study more? Visit our Index here!

Do you prefer video lectures over reading a webpage? Follow us on YouTube to stay updated with the latest video content!

Comments

3 responses to “Electric Field”

  1. Electric Potential – Tru Physics

    […] to a distribution of charges. It is a scalar quantity that plays a crucial role in understanding electric fields and the behavior of charged particles in various […]

    Reply
  2. Chapter 3: Electric Flux – Tru Physics

    […] flux is a measure of the electric field passing through a given surface. It helps us understand how the electric field interacts with […]

    Reply
  3. Chapter 2: Electric Fields – Tru Physics

    […] fields are all around us. An electric field is a region surrounding a charged object where another charged object experiences a force due to […]

    Reply

Have something to add? Leave a comment!