The dimension of magnetic field in `M,L,T and C` (coulomb) is given as

Options

A. (a) `MLT^(-1)C^(-1)`
B. (b) `MT^(2)C^(-2)`
C. ( c ) `MT^(-1)C^(-1)`
D. (d) `MT^(-2)C^(-1)`

Explanation

To find the dimensions of the magnetic field \( B \) in terms of mass \( M \), length \( L \), time \( T \), and charge \( C \), we can start from the formula for the force \( F \) experienced by a charge \( Q \) moving with a velocity \( V \) in a magnetic field \( B \). The relationship is given by:

\[ F = QVB \]

### Step 1: Write the dimensions of force
The dimension of force \( F \) is given by:

\[ [F] = M^1 L^1 T^{-2} \]

### Step 2: Write the dimensions of charge
The dimension of charge \( Q \) (in coulombs) is represented as:

\[ [Q] = C^1 \]

### Step 3: Write the dimensions of velocity
The dimension of velocity \( V \) is given by:

\[ [V] = L^1 T^{-1} \]

### Step 4: Rearranging the formula to find the dimension of \( B \)
From the equation \( F = QVB \), we can rearrange it to find the dimension of the magnetic field \( B \):

\[ B = \frac{F}{QV} \]

### Step 5: Substitute the dimensions into the equation
Substituting the dimensions we have:

\[ [B] = \frac{[F]}{[Q][V]} = \frac{M^1 L^1 T^{-2}}{C^1 \cdot L^1 T^{-1}} \]

### Step 6: Simplifying the dimensions
Now we can simplify the expression:

\[ [B] = \frac{M^1 L^1 T^{-2}}{C^1 \cdot L^1 T^{-1}} = \frac{M^1}{C^1} \cdot \frac{L^1}{L^1} \cdot \frac{T^{-2}}{T^{-1}} = M^1 T^{-1} C^{-1} \]

Thus, the dimension of the magnetic field \( B \) is:

\[ [B] = M^1 T^{-1} C^{-1} \]

### Final Answer
The dimension of the magnetic field \( B \) is \( [B] = M^1 T^{-1} C^{-1} \).

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