What are the fundamental dimensions of magnetic flux density B (Tesla) expressed in M, L, T, and electric current I?
Electronics and Communication Engineering
Measurements and Instrumentation
Difficulty: Easy
Choose an option
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AM I^-1 T^-2
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BM^-1 I^-2 T^-2
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CM L^-3 T^-2
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DM I^-1 T^-3
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EM^0 L^0 T^0 I^1
Answer
Correct Answer: M I^-1 T^-2
Explanation
Introduction / Context:Dimensional analysis checks the physical consistency of equations and units. Magnetic flux density B is measured in Tesla (T), and relating it to base dimensions helps in deriving or verifying electromagnetic formulas in SI units.
Given Data / Assumptions:
- 1 Tesla = 1 Weber per square metre (Wb/m^2) = 1 Newton per (Ampere·metre) (N/(A·m)).
- Newton N has dimensions M L T^-2.
- We examine B in terms of M, L, T, and I.
Concept / Approach:Starting from B = N/(A·m), insert dimensions for N and simplify. No length L remains in the numerator after cancellation; the current appears in the denominator as I^1. This produces the standard result used in electromagnetic derivations, e.g., Lorentz force F = q v × B and Ampere's law in SI.
Step-by-Step Solution:
B = N / (A·m).[N] = M L T^-2; divide by A (current I) and by m (length L).Thus [B] = (M L T^-2) / (I L) = M I^-1 T^-2.Verification / Alternative check:
Using B = Wb/m^2 and Wb = V·s = (kg·m^2·s^-3·A^-1)·s gives the same dimensional result after simplification.Why Other Options Are Wrong:
Options with L terms or different powers of I or T do not match the base definition N/(A·m).Common Pitfalls:
Forgetting that N includes L in the numerator and that an extra L in the denominator comes from the ”per metre”.Final Answer:
M I^-1 T^-2