The dimensional formula of magnetic flux density is :

Options

A. `M^(1)L^(2)T^(1)I^(-1)`
B. `M^(1)T^(-2)I^(-1)`
C. `M^(1)L^(2)T^(-2)I^(-1)`
D. `M^(1)L^(1)T^(-2)I^(-1)`

Answer

To find the dimensional formula of magnetic flux density, we can follow these steps:

### Step 1: Understand Magnetic Flux Density
Magnetic flux density (often represented as \( B \)) is defined as the magnetic flux (\( \Phi \)) per unit area (\( A \)). The formula can be expressed as:
\[ B = \frac{\Phi}{A} \]

### Step 2: Define Magnetic Flux
Magnetic flux (\( \Phi \)) is defined as the product of the magnetic field (\( B \)) and the area (\( A \)):
\[ \Phi = B \cdot A \]

### Step 3: Substitute Magnetic Flux in the Flux Density Formula
Now, substituting the expression for magnetic flux into the formula for magnetic flux density, we get:
\[ B = \frac{B \cdot A}{A} \]
This simplifies to:
\[ B = B \]
This shows that the magnetic flux density is directly related to the magnetic field.

### Step 4: Determine the Dimensional Formula of Magnetic Field
The dimensional formula for magnetic field (\( B \)) can be derived from the force experienced by a charge in a magnetic field. The magnetic field is defined in terms of force per unit charge per unit velocity:
\[ B = \frac{F}{q \cdot v} \]
Where:
- \( F \) (force) has the dimensional formula \( [M L T^{-2}] \)
- \( q \) (charge) has the dimensional formula \( [I T] \)
- \( v \) (velocity) has the dimensional formula \( [L T^{-1}] \)

### Step 5: Combine the Dimensional Formulas
Now, substituting these into the equation for \( B \):
\[ B = \frac{[M L T^{-2}]}{[I T] \cdot [L T^{-1}]} \]
This simplifies to:
\[ B = \frac{[M L T^{-2}]}{[I L T^{-2}]} = [M I^{-1} T^{-2}] \]

### Step 6: Conclusion
Thus, the dimensional formula for magnetic flux density is:
\[ [B] = [M^1 L^0 T^{-2} I^{-1}] \]

### Final Answer
The dimensional formula of magnetic flux density is:
\[ [M^1 T^{-2} I^{-1}] \]

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