Question

If coulomb is also a fundamental quantity with dimension [C], then the dimensions of magnetic field strength is-
1. [M1T-2C-1]
2. [M1T-1C-1]
3. [M2T-1C1]
4. [M1T2C2]

Answer 1

Correct Answer - Option 2 : [M1T-1C-1]

The correct answer is option 2) i.e. [M1T-1C-1]

CONCEPT:

• ​Fundamental quantity: A quantity that can be measured is called a physical quantity. Fundamental quantities are those which cannot be expressed or measured in terms of other physical quantities. 
• The seven fundamental quantities along with their dimensions are as follows:

Fundamental quantity	Dimension
Time	T
Mass	M
Electric current	A
Thermodynamic temperature	K
Amount of substance	mol
Luminous intensity	cd
Length	L

EXPLANATION:

• A charged particle moving relative to a magnetic field experiences a magnetic force due to the magnetic field. The magnitude of this force is given by

F = qvB

Where F is the magnetic force, q is the magnitude of charge, v is the velocity and B is the magnetic field strength.

• Dimension of charge, q = [C]
• Dimension of velocity, v = [L¹T^-1]
• Dimension of force, F = [M¹L¹T^-2]

\(\Rightarrow B = \frac{F}{qv}\)

\(\Rightarrow B = \frac{[M^1L^1T^{-2}]}{[C^1][L^1T^{-1}]} = [M^1T^{-1}C^{-1}]\)