The dimensions of magnetic field in M, L, T and C (Coulomb)...

The dimensions of magnetic field in $M, L, T$ and $C$ (Coulomb) is given as
(A) $\left[M L T^{-1} C^{-1}\right]$
(B) $\left[M T^{2} C^{-2}\right]$
(C) $\left[M T^{-1} C^{-1}\right]$
(D) $\left[M T^{-2} C^{-1}\right]$

Key Concepts

Lorentz Force Law

The Lorentz force law, which states that the force on a charged particle moving in a magnetic field is given by F = q(v × B), provides a direct relationship between the magnetic field, the charge, and the resulting force. This relationship is crucial for determining the dimensional formula of the magnetic field by equating the dimensions on both sides of the equation.

Magnetic Field

In the context of electromagnetism, the magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. The magnetic field is often measured in teslas in SI units, and its dimensional analysis typically involves expressing it in terms of mass, length, time, and charge or current.

Dimensional Analysis

Dimensional analysis is a method used in physics to express a physical quantity in terms of its basic unit dimensions such as mass, length, time, and charge. This technique helps to check the consistency of equations, convert between different unit systems, and deduce relationships between physical quantities.

SI Base Units

The International System of Units (SI) defines a set of base units for fundamental quantities like mass (kg), length (m), time (s), and electric current (A), from which all other units, including those for electromagnetism, are derived. Understanding these units is essential for expressing derived quantities in terms of fundamental dimensions.

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