Electric Field – Class 12 | Chapter – 1 | Physics Short Notes Series PDF for NEET & JEE

Electric Field: The electric field is a concept in electromagnetism that describes the force that a charged particle experiences in response to an electric field. It is a vector field that is represented by a set of vectors at each point in space, indicating the direction and magnitude of the force that would be experienced by a positive test charge at that point.

Electric Field

The electric field at a point is proportional to the gradient of the electric potential, which is the energy per unit charge required to bring a test charge from infinity to that point. The electric potential is a scalar field, which means that it only has a magnitude at each point, but not a direction. The electric field can be calculated as the negative gradient of the electric potential.

The electric field is created by charged objects, such as electrons or ions, and it can affect other charged objects in the surrounding space. For example, an electric field can cause a charged particle to move, change direction, or accelerate, and it can also cause changes in the polarization of dielectric materials.

The electric field can be visualized as field lines, which are lines that represent the direction of the field at each point. The strength of the electric field can be represented by the spacing of the field lines, with closer lines indicating a stronger field and farther lines indicating a weaker field.

It’s important to note that the electric field is not a physical object, but rather a mathematical representation of the force that a charged particle would experience in response to the presence of charged objects. Nevertheless, the electric field plays a crucial role in many physical phenomena, such as the behavior of electric circuits, the behavior of charged particles in electric and magnetic fields, and the interaction of charged particles with electromagnetic waves.

Formula of Electric Field

The formula of electric field is given as;

E = F /Q

Where,

E is the electric field.
F is a force.
Q is the charge.

How to Find Electric Field Using Gauss law?

To use Gauss’s Law to find the electric field, you need to follow these steps:

• Choose a closed surface: Gauss’s Law relates the electric field to the charge enclosed within a closed surface, so you need to choose a closed surface that contains the charge you want to find the electric field of. This surface can be any shape, such as a sphere, a cylinder, or a flat surface, but it must be closed and have a well-defined area.
• Calculate the electric flux: The electric flux through the surface is defined as the dot product of the electric field and the surface normal at each point on the surface, integrated over the entire surface. The electric flux can be calculated using the following equation:

  φ = ∫E⋅dA,

where E is the electric field, dA is a differential area element on the surface, and the integral is taken over the entire surface.

• Relate the electric flux to the charge enclosed: Gauss’s Law states that the electric flux through the surface is proportional to the charge enclosed within the surface. This relationship can be written as:

  φ = Q/ε0,

where Q is the charge enclosed within the surface, and ε0 is the electric constant (also known as the vacuum permittivity).

• Solve for the electric field: Solving for the electric field, we have:

  E = Q/(ε0A),

where A is the area of the surface. This equation gives us the magnitude of the electric field at any point on the surface, and the direction can be found by taking the surface normal.

It’s important to note that Gauss’s Law only works if the charge distribution is symmetric with respect to the surface, as it is a relationship between the electric field and the charge enclosed within a closed surface. In cases where the charge distribution is not symmetric, other methods, such as the method of images, may need to be used to find the electric field.

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By Team Learning Mantras