JEE Main Shortcuts and Tricks

• Magnetic susceptibility (χ):

• χ = (M / H), where M is the magnetization and H is the magnetic field strength.

• χ is a dimensionless quantity that indicates the degree to which a material is magnetized.

• For diamagnetic materials, χ < 0, for paramagnetic materials, χ > 0, and for ferromagnetic materials, χ » 0.

• Relative permeability (μr):

• μr = μ / μ₀, where μ is the permeability of the material and μ₀ is the permeability of free space.

• μr is a dimensionless quantity that indicates the degree to which a material is more permeable to magnetic fields than free space.

• For diamagnetic materials, μr < 1, for paramagnetic materials, μr > 1, and for ferromagnetic materials, μr » 1.

• Saturation magnetization (Ms):

• Ms is the maximum magnetization that a material can achieve when subjected to a sufficiently strong magnetic field.

• Ms is a material property that depends on the atomic and electronic structure of the material.

• For ferromagnetic materials, Ms is typically very high, while for diamagnetic and paramagnetic materials, Ms is very small.

• Curie temperature (Tc):

• Tc is the temperature at which a ferromagnetic material undergoes a phase transition to a paramagnetic state. Below Tc, the material is ferromagnetic, while above Tc, it is paramagnetic. Tc is a material property that depends on the exchange interactions between the atoms in the material.

• Hysteresis loss (Wh):

• Hysteresis loss is the energy lost when a ferromagnetic material is subjected to a cyclic magnetic field.

• Hysteresis loops measure hysteresis loss, which can be used to characterize the magnetic properties of a material.

CBSE Board Exams Shortcuts and Tricks

• Magnetic field due to a current-carrying wire:

• B = μ₀I / (2πr)

• B is the magnetic field strength at a distance r from a long, straight current-carrying wire.

• B is directly proportional to the current I flowing through the wire and inversely proportional to the distance r from the wire.

• Magnetic field due to a solenoid:

• B = μ₀nI

• B is the magnetic field strength inside a solenoid with n turns per unit length and current I flowing through it.

• B is directly proportional to the number of turns per unit length n and the current I flowing through the solenoid.

• Magnetic field due to a bar magnet:

• B = μ₀(2M / 4πr³)

• B is the magnetic field strength at a distance r from a bar magnet with magnetic moment M.

• B is proportional to the magnetic moment of the bar magnet, which depends on the strength and arrangement of the magnetic poles within the magnet.

• Magnetic moment of a current loop:

• m = IA

• m is the magnetic moment of a current loop with current I flowing through a loop of area A.

• The magnetic moment is a vector quantity that describes the strength and direction of the magnetic field produced by the current loop.

• Magnetic moment of a bar magnet:

• m = MLV

• m is the magnetic moment of a bar magnet with magnetic moment M, length L, and volume V.

• The magnetic moment of a bar magnet is related to the magnet’s magnetic poles and its geometric properties.

• Gauss’s law for magnetism: ∮B⋅dA = 0

• This law states that the net magnetic flux through any closed surface is always zero.

• It is analogous to Gauss’s law for electric fields and implies that magnetic monopoles, or isolated magnetic poles, do not exist.

• Ampère’s law for magnetism: ∮B⋅dl = μ₀Ienc

• This law relates the magnetic field around a closed loop to the total electric current flowing through the loop. -It enables the calculation of magnetic fields generated by current-carrying conductors and provides a mathematical tool for analyzing various magnetic configurations.