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The Dimensional formula of magnetic ener...

The Dimensional formula of magnetic energy density is ?

A

`MLT ^(-2) A ^(-1)`

B

`ML T^(-2) A ^(-1)`

C

`ML ^(2) T ^(-3) A ^(-2)`

D

`ML ^(-1) T ^(-2)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the dimensional formula of magnetic energy density, we can follow these steps: ### Step 1: Understand the Concept of Magnetic Energy Density Magnetic energy density is defined as the amount of magnetic energy stored in a unit volume. Therefore, it can be expressed mathematically as: \[ \text{Magnetic Energy Density} = \frac{\text{Magnetic Energy}}{\text{Volume}} \] ### Step 2: Determine the Dimensional Formula of Magnetic Energy Magnetic energy is a form of energy, and the dimensional formula for energy is the same as that for work. The dimensional formula for work (or energy) is given by: \[ \text{Energy} = \text{Force} \times \text{Displacement} \] The dimensional formula for force is: \[ \text{Force} = \text{Mass} \times \text{Acceleration} = MLT^{-2} \] Thus, the dimensional formula for energy becomes: \[ \text{Energy} = \text{Force} \times \text{Displacement} = MLT^{-2} \times L = ML^2T^{-2} \] ### Step 3: Determine the Dimensional Formula of Volume The volume of an object is given by: \[ \text{Volume} = \text{Length}^3 = L^3 \] ### Step 4: Combine the Formulas to Find Magnetic Energy Density Now, substituting the dimensional formula for magnetic energy and volume into the equation for magnetic energy density, we have: \[ \text{Magnetic Energy Density} = \frac{ML^2T^{-2}}{L^3} \] This simplifies to: \[ \text{Magnetic Energy Density} = ML^{-1}T^{-2} \] ### Step 5: Final Result Thus, the dimensional formula of magnetic energy density is: \[ \text{Dimensional Formula} = ML^{-1}T^{-2} \] ### Conclusion From the given options, the correct answer is: **Option 4: \( ML^{-1}T^{-2} \)** ---

To find the dimensional formula of magnetic energy density, we can follow these steps: ### Step 1: Understand the Concept of Magnetic Energy Density Magnetic energy density is defined as the amount of magnetic energy stored in a unit volume. Therefore, it can be expressed mathematically as: \[ \text{Magnetic Energy Density} = \frac{\text{Magnetic Energy}}{\text{Volume}} \] ...
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