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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:

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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:

  1. Identify the positions of the charges.
  2. Calculate the electric potential due to each charge at the midpoint.
  3. Sum the potentials to find the total electric potential at the midpoint.

2. Relevant Concepts

The electric potential V V due to a point charge q q at a distance r r is given by the formula: V=kqr V = \frac{k \cdot q}{r} where k k is the Coulomb's constant (k8.99×109N m2/C2 k \approx 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 ).

3. Analysis and Detail

  1. Position of Charges:

    • Let the two charges +q +q and q -q be located at points d -d and +d +d on the x-axis, respectively.
    • The midpoint M M is at the origin (0,0) (0,0) .
  2. Distance from Midpoint:

    • The distance from the midpoint M M to each charge is d d .
  3. Electric Potential at Midpoint:

    • The potential due to charge +q +q : V1=kqd V_1 = \frac{k \cdot q}{d}
    • The potential due to charge q -q : V2=k(q)d=kqd V_2 = \frac{k \cdot (-q)}{d} = -\frac{k \cdot q}{d}
  4. Total Electric Potential:

    • Sum the potentials: Vtotal=V1+V2=kqdkqd=0 V_{\text{total}} = V_1 + V_2 = \frac{k \cdot q}{d} - \frac{k \cdot q}{d} = 0

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: V=0V V = 0 \, \text{V}

This problem has been solved

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