The dimensions [MLT-2A-2] belong to the:
- Magnetic flux
- Self Inductance
- Magnetic permeability
- Electric permittivity
The Correct Option is C
Solution and Explanation
The given dimensions are [MLT-2A-2]. We need to determine which physical quantity corresponds to these dimensions.
Let's break down the dimensions:
- M: Mass, dimension [ M ]
- L: Length, dimension [ L ]
- T: Time, dimension [ T ]
- A: Electric current, dimension [ A ]
The dimensions [MLT-2A-2] can be analyzed as follows:
1. The term [MLT-2] represents force, which is derived from Newton's second law: F = ma, where F is force, m is mass, and a is acceleration. Acceleration has dimensions [LT-2], thus force has dimensions [MLT-2].
2. The additional factor A-2 indicates a relationship with the square of current. This suggests an electromagnetic property involving current in the denominator.
Now, consider the options:
Magnetic flux has dimensions [ M0L2T-2A-1 ] which does not match.
Self Inductance has dimensions [ M1L2T-2A-2 ], but typically concerns current and voltage without the exact form of force per current squared.
Magnetic permeability: It quantifies the ability of a material to support the formation of a magnetic field within itself and typically has dimensions matching the form [MLT-2A-2], as it involves the response of force per unit current per unit length squared to a magnetic field.
Electric permittivity has dimensions [ M-1L-3T4A2 ].
Therefore, the correct answer is: Magnetic permeability.
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Concepts Used:
Electric Field
Electric Field is the electric force experienced by a unit charge.
The electric force is calculated using the coulomb's law, whose formula is:
\(F=k\dfrac{|q_{1}q_{2}|}{r^{2}}\)
While substituting q2 as 1, electric field becomes:
\(E=k\dfrac{|q_{1}|}{r^{2}}\)
SI unit of Electric Field is V/m (Volt per meter).