Find `V_(ba)`, if `12 J` of work has to be done against an electric field to take a charge of `10^-2` C from a to b.

Explanation

To find the potential difference \( V_{ba} \) when \( 12 \, \text{J} \) of work is done against an electric field to move a charge of \( 10^{-2} \, \text{C} \) from point A to point B, we can follow these steps:

### Step 1: Understand the relationship between work, charge, and potential difference.
The work done \( W \) in moving a charge \( Q \) through a potential difference \( V_{ba} \) is given by the formula:
\[ W = Q \cdot V_{ba} \]
Where:
- \( W \) is the work done (in joules),
- \( Q \) is the charge (in coulombs),
- \( V_{ba} \) is the potential difference between points B and A (in volts).

### Step 2: Rearrange the formula to find \( V_{ba} \).
We can rearrange the formula to solve for \( V_{ba} \):
\[ V_{ba} = \frac{W}{Q} \]

### Step 3: Substitute the known values into the equation.
We know:
- \( W = 12 \, \text{J} \)
- \( Q = 10^{-2} \, \text{C} \)

Substituting these values into the equation gives:
\[ V_{ba} = \frac{12 \, \text{J}}{10^{-2} \, \text{C}} \]

### Step 4: Calculate \( V_{ba} \).
Now, perform the calculation:
\[ V_{ba} = \frac{12}{10^{-2}} = 12 \times 10^{2} = 1200 \, \text{V} \]

### Final Answer:
Thus, the potential difference \( V_{ba} \) is:
\[ V_{ba} = 1200 \, \text{V} \]

---