What is the Dimensional Formula of Magnetic Field (B)?

To derive the dimension, we use the easiest and most fundamental formula in magnetism: The Lorentz Magnetic Force Equation. This formula calculates the massive force (F) experienced by a moving electric charge (q) traveling at a velocity (v) through a magnetic field (B).

The formula is: F = qvB (Assuming the angle is 90 degrees, so sinθ = 1).

Step 1: Rearrange the formula to isolate the Magnetic Field (B): B = F / (q × v)

Step 2: Find the fundamental dimensions for the other variables:

• Dimension of Force (F) = [M¹ L¹ T⁻²]
• Dimension of Velocity (v) = [L¹ T⁻¹]
• Dimension of Charge (q). Charge is Current × Time, so its dimension is [A¹ T¹].

Step 3: Put these dimensions into the rearranged equation: B = [M¹ L¹ T⁻²] / ( [A¹ T¹] × [L¹ T⁻¹] )

Step 4: Simplify the denominator: The [T¹] and [T⁻¹] in the denominator perfectly cancel each other out (1 - 1 = 0). The denominator simplifies to just: [A¹ L¹].

Step 5: Divide the numerator by the simplified denominator: B = [M¹ L¹ T⁻²] / [A¹ L¹]

• The [L¹] on top and bottom perfectly cancel out (making L⁰).
• Bring the [A¹] up to become [A⁻¹].

Final Dimension of Magnetic Field (B) = [M¹ L⁰ T⁻² A⁻¹].