Dimensions of Magnetic Field – Formula, Derivation, Units & Uses

The Dimensions of Magnetic Field are a key topic in JEE Main Physics, especially for dimensional analysis and unit conversion in electromagnetism. The magnetic field concept helps in understanding forces on moving charges and current-carrying conductors. JEE students must know its formula, dimensions, and where it applies in physical problems.

Understanding the dimensions of magnetic field allows you to verify equations, compare units like Tesla and Gauss, and distinguish magnetic field intensity from induction and flux. Mastery of this area is crucial for quick problem-solving during JEE paper attempts.

In electromagnetism, the magnetic field is represented by B (magnetic induction). It acts perpendicularly to both current and resultant force, and always follows the right-hand rule. Magnetic field intensity and related terms often confuse students, so learning their dimensions and differences is necessary.

Dimensional Formula of Magnetic Field (B) and Its Derivation

In SI units, the dimensions of magnetic field (magnetic induction, B) are derived from the Lorentz force: F = q(v × B). Here, F is force, q is charge, v is velocity, and B is magnetic field.

Derivation:
Start with F = qvB sinθ (take θ = 90° for max value). Rearranging gives B = F/(qv). Substitute dimensions: [B] = [M¹L¹T^-2]/([I¹T¹][L¹T^-1]) = [M¹L⁰T^-2I^-1].

Hence, the dimensional formula for the magnetic field B is [M¹L⁰T^-2I^-1]. This matches JEE and NCERT expectations.

Units, Measurement and Related Variants for Dimensions of Magnetic Field

The primary SI unit for the dimensions of magnetic field is Tesla (T), while the CGS unit is Gauss (G), where 1 T = 10⁴ G. Both units represent magnetic field induction, or magnetic field density (B).

This table shows how SI and CGS units relate for different magnetic quantities. Knowing conversions is vital for JEE numericals and unit checks. Explore more about units and measurement for expert strategies.

Magnetic field is a vector quantity, meaning it has both magnitude and direction in three-dimensional space. Always apply the right-hand thumb rule for direction sense and remember vector rules in vector questions.

Comparison: Dimensions of Magnetic Field Intensity, Permeability, Energy Density

It's common for students to confuse the dimensions of magnetic field (B) with magnetic field intensity (H), magnetic permeability, or energy density of a magnetic field. Each has its own definition and dimensional formula.

Each term above appears in standard JEE Main questions or formula derivations. Learn about magnetic permeability for detailed applications and differences in their dimensions.

• The dimensions of magnetic flux differ from the field itself.
• Magnetic field energy density involves B squared in its formula.
• Field intensity (H) is not the same as induction (B).

Misidentifying these quantities can lead to incorrect unit or dimension analysis. Always clarify what is being asked, especially when using dimensional analysis tools.

Application of Dimensions of Magnetic Field in JEE Problems

Direct questions on dimensions of magnetic field may ask you to compute or check expressions using dimensional consistency. Using B’s formula helps identify errors and verify derived results under principle of homogeneity conditions.

1. Check that units on both sides of an electromagnetism equation match.
2. For formulas like F = BIL, verify [B] using [F] = [B][I][L].
3. Convert Tesla to Gauss using 1 T = 10⁴ G.
4. Apply dimensional analysis to unknown or derived expressions in papers.

Mini Example: In the Biot-Savart Law, dB = (μ₀/4π)·(I dl × r̂)/r², dimensions of dB must reduce to [M¹L⁰T^-2I^-1]. If not, you have a mistake.

The same validation applies when working with Biot-Savart law, Faraday’s law, or field expressions for a solenoid or infinite wire.

For more practice, review units and measurements mock tests and magnetic effects of current and magnetism mock test 2.

• Check formula consistency using dimensions before substituting values.
• Memorize dimensions of B, H, μ, and flux for last-moment revision.
• Avoid mixing up the meaning and formula for B and H in vectors.

Explore worked problems and revision strategies via dimensional analysis and its applications and work energy and power pages.

Vedantu’s expert content team updates these formulas to match JEE standards and includes clear step-by-step logic, not just rote learning.

Summary: The dimensions of magnetic field are [M¹L⁰T^-2I^-1], with the SI unit Tesla. Always distinguish magnetic field B from related terms. Apply dimensional analysis for both revision and error detection. For more clarity, check related concepts like dimensions of electric flux and magnetic effects of current and magnetism.

• Units and dimensions basics for Physics formulas.
• Conceptual review with magnetic field and magnetic force examples.
• Revision with dimensional analysis methods.
• Practice more with magnetic effects of current and magnetism practice paper.
• Explore magnetism revision notes for exam-oriented tips.
• Clarify comparisons via difference between electric field and magnetic field.

Review these pages from Vedantu for systematic JEE-level mastery of electromagnetic field problems.