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What are the fundamental dimensions of magnetic flux density B (Tesla) expressed in M, L, T, and electric current I?

Difficulty: Easy

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
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