Question

A 200 J of work is done in moving a charge 5C from a point A where the potential is - 20 V to another point B where potential is V volt. The value of V at B is

• A. 10 V
• B. 20 V
• C. 40 V
• D. 60 V

Hint:

Always be careful with signs when substituting potential values. Subtracting a negative potential (\( -(-20) \)) becomes addition. Also, ensure the work is done \textbf{on} the charge by an external force to use this specific formula form.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem involves calculating the electric potential at a point based on the work done to move a known charge between two points with a given potential difference.
Step 2: Key Formula or Approach:
The work done (\(W\)) in moving a charge (\(q\)) from point A to point B is given by:
\[ W = q \cdot (V_B - V_A) \] Where:
- \(W\) is the work done (in Joules).
- \(q\) is the magnitude of the charge (in Coulombs).
- \(V_B\) is the potential at final point B.
- \(V_A\) is the potential at initial point A.
Step 3: Detailed Explanation:
Given values:
- Work done, \(W = 200 \text{ J}\).
- Charge, \(q = 5 \text{ C}\).
- Potential at A, \(V_A = -20 \text{ V}\).
- Potential at B, \(V_B = V\).
Substituting these into the formula:
\[ 200 = 5 \cdot (V - (-20)) \]
Divide both sides by 5:
\[ 40 = V + 20 \]
Solving for \(V\):
\[ V = 40 - 20 = 20 \text{ V} \]
Therefore, the value of potential at point B is 20 V.
Step 4: Final Answer:
The potential \(V\) at B is 20 V.