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When a positive q charge is taken from l...

When a positive `q` charge is taken from lower potential to a higher potential point, then its potential energy will

A

decrease

B

increase

C

remains changed

D

become zero

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the situation where a positive charge \( q \) is moved from a point of lower electric potential to a point of higher electric potential. We can follow these steps: ### Step 1: Understand the Concept of Electric Potential Electric potential (V) at a point in an electric field is the amount of work done in bringing a unit positive charge from infinity to that point without any acceleration. When we say a point has a higher potential, it means that it requires more work to bring a charge to that point compared to a point of lower potential. **Hint:** Remember that electric potential is a measure of potential energy per unit charge. ### Step 2: Identify the Initial and Final Potentials Let \( V_i \) be the initial potential (lower potential) and \( V_f \) be the final potential (higher potential). Since \( V_f > V_i \), the difference in potential is given by: \[ \Delta V = V_f - V_i \] **Hint:** The change in potential \( \Delta V \) is positive because you are moving to a higher potential. ### Step 3: Calculate the Change in Potential Energy The change in potential energy (\( \Delta U \)) when moving a charge \( q \) through a potential difference \( \Delta V \) is given by the formula: \[ \Delta U = q \cdot \Delta V \] Substituting the expression for \( \Delta V \): \[ \Delta U = q \cdot (V_f - V_i) \] **Hint:** The change in potential energy is directly proportional to the charge and the potential difference. ### Step 4: Analyze the Sign of the Change in Potential Energy Since \( V_f > V_i \), it follows that \( \Delta V > 0 \). Therefore, the change in potential energy (\( \Delta U \)) will also be positive: \[ \Delta U > 0 \] This indicates that the potential energy of the charge increases when it is moved from a lower potential to a higher potential. **Hint:** A positive change in potential energy means that energy is stored in the system. ### Conclusion When a positive charge \( q \) is taken from a lower potential to a higher potential point, its potential energy increases. **Final Answer:** The potential energy will increase.
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