Question

Dimensional formula of magnetic flux is
1. M² L² T^-3
2. M^-2 I1 L^-1 T^-2
3. M¹ I^-1 L² T^-2
4. M2 L^-2 T-3

Answer 1

Correct Answer - Option 3 : M¹ I^-1 L² T^-2

The correct answer is option 3) i.e. M1 I-1 L2 T-2

CONCEPT:

• Magnetic flux: Magnetic flux is the measure of the number of magnetic field lines passing through a given surface area.

The magnetic flux ϕ is given by:

ϕ = BAcosθ 

Where B is the magnetic field strength, A is the area vector, and θ is the angle made by the area vector with respect to the magnetic field line.

EXPLANATION:

We know, ϕ = BAcosθ 

For dimensional analysis, ϕ = BA

The dimensional formula of A (area) = L²       ----(1)

From lenz's law we know that F = q(v × B) ⇒ B = \(\frac{F}{qv}\)

Force, F = mass × acceleration ⇒ M¹ L¹T^-2      ----(2)

Charge, q = Current × time ⇒ I¹ T¹      ----(3)

Velocity, v ⇒ L¹ T^-1      ----(4)

Substituting (1), (2), (3), and (4) in ϕ = BA

[ϕ] = \(\frac{F}{qv}\)A = \(\frac{M^1 L^1T^{-2} }{(I^1T^1)(L^1T^{-1})} L^2 \) = M1 I-1 L2 T-2