Find the dimensions of
a. electric dipole moment p and
b. magnetic dipole moment M.
The defining equations are `p=q.d and M=IA,`
whre d is distance, A is area, q is charge and I is current.

Explanation

To find the dimensions of the electric dipole moment \( p \) and the magnetic dipole moment \( M \), we will use the given defining equations:

1. **Electric Dipole Moment \( p \)**:
The electric dipole moment is defined as:
\[ p = q \cdot d \]
where \( q \) is the charge and \( d \) is the distance.

- **Step 1**: Identify the dimensions of charge \( q \).
- Charge \( q \) can be expressed in terms of current \( I \) and time \( T \):
\[ q = I \cdot T \]
Therefore, the dimension of charge \( [q] \) is:
\[ [q] = [I][T] = A^1 T^1 \]

- **Step 2**: Identify the dimensions of distance \( d \).
- The dimension of distance \( d \) is:
\[ [d] = L^1 \]

- **Step 3**: Substitute the dimensions of \( q \) and \( d \) into the equation for \( p \):
\[ [p] = [q][d] = (A^1 T^1)(L^1) = A^1 L^1 T^1 \]

Thus, the dimensions of the electric dipole moment \( p \) are:
\[ [p] = A^1 L^1 T^1 \]

2. **Magnetic Dipole Moment \( M \)**:
The magnetic dipole moment is defined as:
\[ M = I \cdot A \]
where \( I \) is the current and \( A \) is the area.

- **Step 4**: Identify the dimensions of area \( A \).
- The area \( A \) can be expressed in terms of length:
\[ [A] = L^2 \]

- **Step 5**: Substitute the dimensions of \( I \) and \( A \) into the equation for \( M \):
\[ [M] = [I][A] = (A^1)(L^2) = A^1 L^2 \]

Thus, the dimensions of the magnetic dipole moment \( M \) are:
\[ [M] = A^1 L^2 \]

### Final Answers:
- The dimensions of the electric dipole moment \( p \) are \( [p] = A^1 L^1 T^1 \).
- The dimensions of the magnetic dipole moment \( M \) are \( [M] = A^1 L^2 \).