Magnetic induction and magnetic flux differ in the dimensions of

Options

A. Mass
B. Electric current
C. Length
D. Time

Answer

To solve the question regarding the difference in dimensions between magnetic induction and magnetic flux, we can follow these steps:

### Step 1: Understand the Definitions
- **Magnetic Flux (Φ)**: It is defined as the product of the magnetic field (B) and the area (A) through which the field lines pass. Mathematically, it is expressed as:
\[ Φ = B \cdot A \]

- **Magnetic Induction (B)**: Also known as magnetic field strength, it represents the amount of magnetic field present in a region.

### Step 2: Identify the Dimensions
- The dimension of magnetic flux (Φ) can be derived from its formula:
\[ Φ = B \cdot A \]
Here, the dimensions of area (A) are:
\[ [A] = L^2 \]
Therefore, the dimension of magnetic flux (Φ) is:
\[ [Φ] = [B] \cdot [A] = [B] \cdot L^2 \]

- The dimension of magnetic induction (B) is typically given as:
\[ [B] = M^1 L^{-1} T^{-2} I^{-1} \]
where M is mass, L is length, T is time, and I is electric current.

### Step 3: Calculate the Dimensions of Magnetic Flux
Using the dimensions of magnetic induction (B) and area (A):
\[ [Φ] = [B] \cdot L^2 = (M^1 L^{-1} T^{-2} I^{-1}) \cdot (L^2) = M^1 L^{1} T^{-2} I^{-1} \]

### Step 4: Compare the Dimensions
Now, we have:
- Dimension of magnetic flux (Φ): \( M^1 L^{1} T^{-2} I^{-1} \)
- Dimension of magnetic induction (B): \( M^1 L^{-1} T^{-2} I^{-1} \)

### Step 5: Identify the Difference
The difference in dimensions between magnetic flux and magnetic induction is due to the area (L²) in the formula for magnetic flux. Specifically, the dimension of length (L) is the factor that differentiates them.

### Conclusion
Thus, the dimensions of magnetic induction and magnetic flux differ in the dimension of length (L).

### Final Answer
The answer is **length (L)**.

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