wo opposite charges of magnitude q are separated by a distance 2d.The electric potential due to these charges at mid of these will by
Question
Question
Two opposite charges of magnitude q are separated by a distance 2d. The electric potential due to these charges at the midpoint will be:
Solution
1. Break Down the Problem
To find the electric potential at the midpoint between two opposite charges, we can break the problem down into the following parts:
- Identify the positions of the charges.
- Calculate the electric potential due to each charge at the midpoint.
- Sum the potentials to find the total electric potential at the midpoint.
2. Relevant Concepts
The electric potential due to a point charge at a distance is given by the formula: where is the Coulomb's constant ().
3. Analysis and Detail
-
Position of Charges:
- Let the two charges and be located at points and on the x-axis, respectively.
- The midpoint is at the origin .
-
Distance from Midpoint:
- The distance from the midpoint to each charge is .
-
Electric Potential at Midpoint:
- The potential due to charge :
- The potential due to charge :
-
Total Electric Potential:
- Sum the potentials:
4. Verify and Summarize
The calculations reveal that the potential due to one charge cancels out the potential due to the other charge at the midpoint. Thus, the total electric potential at the midpoint is zero.
Final Answer
The electric potential at the midpoint between the two opposite charges is:
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