Point A is located 0.25 m away from a charge of `-2.1 xx 10^(-9) C`. Point B is located 0.50 m away from the charge. What is the electric potential difference `V_(B)- V_(A) between these two points ?

Options

A. 19 V
B. 26 V
C. 38 V
D. 76 V

Answer

To find the electric potential difference \( V_B - V_A \) between points A and B, we can follow these steps:

### Step 1: Understand the formula for electric potential
The electric potential \( V \) due to a point charge \( Q \) at a distance \( R \) is given by the formula:
\[ V = \frac{kQ}{R} \]
where \( k \) is Coulomb's constant, approximately \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

### Step 2: Calculate the electric potential at point A
Point A is located 0.25 m away from the charge \( -2.1 \times 10^{-9} \, \text{C} \). Using the formula:
\[ V_A = \frac{kQ}{R_A} = \frac{(9 \times 10^9) \times (-2.1 \times 10^{-9})}{0.25} \]
Calculating this:
\[ V_A = \frac{(9 \times -2.1)}{0.25} = \frac{-18.9}{0.25} = -75.6 \, \text{V} \]

### Step 3: Calculate the electric potential at point B
Point B is located 0.50 m away from the charge. Using the formula:
\[ V_B = \frac{kQ}{R_B} = \frac{(9 \times 10^9) \times (-2.1 \times 10^{-9})}{0.50} \]
Calculating this:
\[ V_B = \frac{(9 \times -2.1)}{0.50} = \frac{-18.9}{0.50} = -37.8 \, \text{V} \]

### Step 4: Calculate the electric potential difference
Now, we can find the potential difference \( V_B - V_A \):
\[ V_B - V_A = -37.8 - (-75.6) = -37.8 + 75.6 = 37.8 \, \text{V} \]

### Final Answer
The electric potential difference \( V_B - V_A \) is:
\[ \boxed{37.8 \, \text{V}} \]