Dimensional Formula of Magnetic Field B

The dimensional formula of a physical quantity represents the expression that shows how the physical quantity is related to the fundamental quantities in terms of their dimensions. The magnetic field is a fundamental concept in electromagnetism and is denoted by the symbol B. It is a vector quantity that represents the strength and direction of the magnetic field at a given point in space.

The dimensional formula of magnetic field B can be derived using the following steps:

Step 1: Identify the Fundamental Quantities
The fundamental quantities in the International System of Units (SI) are mass (M), length (L), time (T), electric current (I), temperature (θ), amount of substance (N), and luminous intensity (J). In the case of the magnetic field, the relevant fundamental quantities are length (L), electric current (I), and time (T).

Step 2: Determine the Relationship
The magnetic field is defined in terms of the force experienced by a charged particle moving in a magnetic field. According to the Lorentz force law, the force experienced by a charged particle (F) is given by the equation:

F = q(v x B)

where q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field. By rearranging the equation, we can express the magnetic field B in terms of the force F, charge q, and velocity v:

B = F / (q v)

Step 3: Write the Dimensional Formula
To write the dimensional formula of magnetic field B, we substitute the dimensions of the fundamental quantities involved. The dimensions of force (F) are [MLT⁻²], charge (q) is [AT], and velocity (v) is [LT⁻¹]. Substituting these dimensions into the equation for B, we get:

[B] = [MLT⁻²] / ([AT] [LT⁻¹])

Simplifying the expression, we find:

[B] = [M¹L¹T⁻²A⁻¹]

Therefore, the dimensional formula of magnetic field B is [M¹L¹T⁻²A⁻¹], which represents the dimensions of mass, length, time, and electric current.

Summary:
To summarize, the dimensional formula of magnetic field B is [M¹L¹T⁻²A⁻¹], where M represents mass, L represents length, T represents time, and A represents electric current. The magnetic field is a vector quantity that is defined in terms of the force experienced by a charged particle moving in a magnetic field, and its dimensional formula can be derived by analyzing the dimensions of the fundamental quantities involved in its definition.