Which of the following statement(s) `is//are` correct ?

Options

A. Units of magnetic field B can be written as `(N)/(A-m)`
B. Units of magnetic permeability `mu_(0)` can be wirtten as` (N)/(A^(2))`
C. Units of magnetic flux `phi` can be written as `(N)/(A-m^(2))`
D. Units of magnetic flux can be `(N-m^(2))/(A)`

Answer

To determine which statements are correct regarding the units of magnetic field, magnetic permeability, and magnetic flux, we will analyze each option step by step.

### Step 1: Analyze Option A
**Statement:** The units of magnetic field can be given as Newton per ampere meter.

1. **Magnetic Force Formula:** The magnetic force (F) on a charge (Q) moving with velocity (V) in a magnetic field (B) is given by:
\[ F = Q \cdot V \cdot B \cdot \sin(\theta) \]
where \(\sin(\theta)\) is unitless.

2. **Units of Each Quantity:**
- Force (F) has units of Newton (N).
- Charge (Q) has units of Coulomb (C).
- Velocity (V) has units of meter per second (m/s).

3. **Rearranging for Magnetic Field (B):**
\[ B = \frac{F}{Q \cdot V} \]
Substituting the units:
\[ B = \frac{N}{C \cdot \frac{m}{s}} = \frac{N \cdot s}{C \cdot m} \]

4. **Converting Coulomb per second to Ampere:**
\[ 1 \, \text{A} = 1 \, \frac{C}{s} \]
Therefore, we can rewrite:
\[ B = \frac{N}{A \cdot m} \]
This confirms that the unit of magnetic field is indeed:
\[ B = \frac{N}{A \cdot m} \]
Thus, **Option A is correct.**

### Step 2: Analyze Option B
**Statement:** The units of magnetic permeability (\(\mu_0\)) can be given as Newton per ampere squared.

1. **Magnetic Field Relation:** The magnetic field (B) can also be expressed in terms of magnetic permeability (\(\mu\)) and magnetic intensity (H):
\[ B = \mu \cdot H \]

2. **Units of Magnetic Intensity (H):**
- The unit of H is Ampere per meter (A/m).

3. **Rearranging for Magnetic Permeability (\(\mu\)):**
\[ \mu = \frac{B}{H} \]
Substituting the units:
\[ \mu = \frac{\frac{N}{A \cdot m}}{\frac{A}{m}} = \frac{N}{A^2} \]
This confirms that the unit of magnetic permeability is:
\[ \mu = \frac{N}{A^2} \]
Thus, **Option B is correct.**

### Step 3: Analyze Option C
**Statement:** The units of magnetic flux can be given as Newton meter per ampere.

1. **Magnetic Flux Formula:** Magnetic flux (\(\Phi\)) is given by:
\[ \Phi = B \cdot A \]
where A is the area.

2. **Units of Area (A):** The unit of area is meter squared (m²).

3. **Calculating Units of Magnetic Flux:**
\[ \Phi = B \cdot A = \left(\frac{N}{A \cdot m}\right) \cdot (m^2) = \frac{N \cdot m}{A} \]
This does not match the statement given in Option C. Thus, **Option C is incorrect.**

### Step 4: Analyze Option D
**Statement:** The units of magnetic field can be given as Tesla.

1. **Definition of Tesla:** The Tesla (T) is defined as:
\[ 1 \, T = 1 \, \frac{N}{A \cdot m} \]
Therefore, this statement is true, but it does not match the specific unit mentioned in the question.

2. **Conclusion for Option D:** Since the statement does not match the specific unit mentioned, **Option D is incorrect.**

### Final Conclusion
The correct options are:
- **Option A:** Correct
- **Option B:** Correct
- **Option C:** Incorrect
- **Option D:** Incorrect

### Summary of Correct Answers
Only options A and B are correct.

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