Unit of magnetic induction field B is

Options

A. tesla
B. `Wb m^(-2)`
C. `N (Am)^(-1)`
D. all the above

Answer

To determine the unit of the magnetic induction field \( B \), we can follow these steps:

### Step 1: Identify the SI Unit of Magnetic Field
The magnetic induction field \( B \) is commonly known as the magnetic field. The SI unit of the magnetic field is the **Tesla (T)**.

### Step 2: Relate Magnetic Field to Magnetic Flux
The magnetic flux \( \Phi \) is related to the magnetic field \( B \) and the area \( A \) through the formula:
\[ \Phi = B \cdot A \]
From this equation, we can express \( B \) as:
\[ B = \frac{\Phi}{A} \]

### Step 3: Identify the Units of Magnetic Flux and Area
The unit of magnetic flux \( \Phi \) is the **Weber (Wb)**, and the unit of area \( A \) is **square meters (m²)**. Therefore, we can express the unit of \( B \) as:
\[ B = \frac{\text{Weber}}{\text{meter}^2} = \text{Weber} \cdot \text{meter}^{-2} \]

### Step 4: Use the Force on a Conductor Formula
The magnetic field can also be derived from the force acting on a conductor carrying current. The force \( F \) on a conductor of length \( L \) carrying current \( I \) in a magnetic field \( B \) is given by:
\[ F = B \cdot I \cdot L \]
Rearranging this gives:
\[ B = \frac{F}{I \cdot L} \]

### Step 5: Identify the Units of Force, Current, and Length
The unit of force \( F \) is the **Newton (N)**, the unit of current \( I \) is the **Ampere (A)**, and the unit of length \( L \) is the **meter (m)**. Thus, we can express the unit of \( B \) as:
\[ B = \frac{\text{Newton}}{\text{Ampere} \cdot \text{meter}} = \text{Newton} \cdot \text{Ampere}^{-1} \cdot \text{meter}^{-1} \]

### Step 6: Conclusion
From the above derivations, we have found that the unit of magnetic induction field \( B \) can be expressed in multiple ways:
1. Tesla (T)
2. Weber per square meter (Wb/m²)
3. Newton per Ampere meter (N/(A·m))

Thus, the correct answer is that the unit of magnetic induction field \( B \) is **all of the above**.

### Final Answer:
The unit of magnetic induction field \( B \) is **Tesla (T)**, **Weber per square meter (Wb/m²)**, and **Newton per Ampere meter (N/(A·m))**. Therefore, the answer is **all of the above**.

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