Question

The dimensions [MLT^-2A^-2] belong to the:

• A. Magnetic flux
• B. Self Inductance
• C. Magnetic permeability
• D. Electric permittivity

Answer 1

The Correct Option is C

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.