Given a square of side length a = 6 cm. We place a charged particle at each corner, three of them carry +7 nC of charge and one carries the same amount of negative charge. What is the electric potential at the center of the square? Choose V = 0 V for a position very far from the square.
electric potential is a scalar, so you add each.
V= kq1/d+kq2/d + ... notice the negative just cancels from one of the positive.
= 14E-9 * k/d where d= 1/2 diagonal length.
Dealing with scalars is nice.
To find the electric potential at the center of the square, we need to calculate the contribution of each charged particle and sum them up.
First, let's consider the positive charges. Since there are three charged particles with +7 nC charge each, their total charge is 3 * 7 nC = 21 nC. The electric potential due to positive charges is given by the formula:
V_positive = k * (Q / r)
Where:
- V_positive is the electric potential due to positive charges
- k is the electrostatic constant (approximately 9 * 10^9 N m^2/C^2)
- Q is the total charge (21 nC in this case)
- r is the distance from the center of the square to the charged particle (which is the side length divided by 2, so r = a/2)
Now, let's consider the negative charge. Its contribution to the electric potential is the opposite in sign, as it is negative. So, V_negative = -k * (Q / r).
To find the total electric potential at the center, we need to calculate the sum of the contributions from the positive and negative charges:
V_total = V_positive + V_negative
Substituting in the values, we have:
V_positive = k * (21 nC / (6 cm / 2))
V_negative = -k * (7 nC / (6 cm / 2))
Finally, we can calculate V_total:
V_total = V_positive + V_negative
Note: Remember to convert all units to SI units (meters and Coulombs) before performing the calculations and preserve the signs of the charges during calculation.