Electricity & Magnetism Class Notes

A mathematical operation that combines two vectors and results in a scalar value. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them.

The scalar product of two vectors is zero when they are perpendicular to each other. This is because the cosine of 90 degrees is zero.

The angle between two vectors can be calculated using the scalar product and the magnitudes of the vectors. The formula involves dividing the scalar product by the product of the magnitudes.

The work done by a force on an object is equal to the scalar product of the force and the displacement of the object.

A vector product (also known as cross product) is a binary operation on two vectors in three-dimensional space that results in a vector perpendicular to both input vectors.

In a three-dimensional space, a right-hand coordinate system is defined as a system where the thumb points in the direction of the resulting vector when the fingers curl from the first vector to the second vector.

The magnitude of the cross product of two vectors is equal to the product of their magnitudes and the sine of the angle between them.

The cross product of two parallel vectors is a zero vector. This is because the sine of 0 degrees is zero.

The force exerted by a primary charge (q) on a small probe charge (q0) divided by the value of the probe charge. It describes the electric influence of the primary charge at a specific point in space.

The electric field at a point in space due to a single stationary point charge is determined by Coulomb's Law and is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance from the charge.

The unit of electric field strength is Newton per Coulomb (N/C). This represents the force exerted on a charge of one Coulomb in the field.

The electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

A small test charge placed in an electric field will experience a force due to the field. This force is proportional to the magnitude of the test charge and the strength of the electric field.

The electric field created by a point charge can be described by a vector quantity. This vector represents both the magnitude and direction of the electric force at a point in space.

The ratio of the force experienced by a probe charge (q0) to the value of the probe charge (q0) is a characteristic of the primary charge (q) and independent of the probe charge. This ratio defines the electric field.

The electric field strength created by a point charge decreases with increasing distance from the charge. This inverse square relation is a result of the geometric spreading of the field.

The electric field produced by a dipole at a point a distance 'L' away from each charge and along the dipole's axis.

The electric field produced by a dipole at a point a distance 'L' away from each charge and perpendicular to the dipole's axis.

A method to calculate the electric field generated by any charge distribution by treating each infinitesimally small element of the distribution as a point charge and summing the contributions of all these point charges.

The process of dividing a continuous charge distribution into infinitesimally small elements, each acting as a point charge, to calculate the electric field generated by the distribution.

The electric field due to two identical positive charges at a point equidistant from both charges.

A vector representing the change in position or displacement of a charged particle in an electric field.

The electric field at a specific point in space due to a collection of charges, calculated by summing the electric fields produced by each individual charge.

The electric field produced by a dipole, characterized by its unique directional and magnitude properties.

The number of electric field lines passing through a given surface. It's a scalar quantity measured in units of N⋅m²/C.

The vector representing the area of a surface, with its direction perpendicular to the surface.

The change in electric flux through a small surface element. It's the product of the electric field component perpendicular to the surface and the area of the element.

The total electric flux passing through a closed surface. Calculated by integrating the dot product of the electric field and the area vector over the entire surface.

The electric flux through a closed surface is proportional to the net electric charge enclosed within the surface. The proportionality constant is 1/ε₀, where ε₀ is the permittivity of free space.

The electric field lines are denser in areas where the electric field strength is higher.

The force per unit charge experienced by a test charge placed in an electric field.

An imaginary surface used to calculate the electric flux. It can be any shape, but it's often chosen to simplify calculations.

The electric field inside a uniformly charged sphere is zero. This is because the charges distribute symmetrically, canceling out the field at every point inside.

The electric field outside a uniformly charged sphere is the same as if all the charge were concentrated at the center of the sphere.

A non-conducting plane with uniform charge density (σ) creates an electric field that is perpendicular to the plane and has a constant magnitude of σ/(2ε0).

The electric field between two parallel charged plates is uniform and its magnitude is equal to the charge density (σ) divided by the permittivity of free space (ε0).

The unit of charge is the Coulomb (C). It's the fundamental unit for measuring the amount of electric charge.

Gauss's Theorem (GT) states that the total electric flux through a closed surface is proportional to the enclosed electric charge.

Coulomb's Law describes the force between two point charges, while Gauss's Theorem relates the electric flux through a closed surface to the enclosed charge. Both laws are fundamental to understanding electromagnetism.

It is a mathematical relationship between electric flux and the enclosed charge in a closed surface. It's similar to saying the total amount of water flowing out of a pipe is determined by the amount of water inside the pipe.

Gauss's Theorem can be used to calculate the electric field for continuous charge distributions with a high degree of symmetry, such as a sphere or a cylinder.

The GT is used to derive Coulomb's Law, demonstrating that both concepts are strongly interconnected.

The Gaussian surface must be chosen such that the electric field is constant and perpendicular to the surface. This maximizes the simplicity of the calculations.

The electric field inside a charged spherical shell is zero. This is because the enclosed charge is zero within the shell, according to Gauss's Theorem.

For a charged spherical shell, the electric field outside the shell is the same as if all the charge was concentrated at the center of the sphere. This is a consequence of Gauss's Theorem and the radial symmetry of the charge distribution.