Find the electric potential at the centre of the square of side 1m at the four corners of charges of q1, q2,q3,and q4 are placed having values 3×10^-8C,-3×10^-8C,-5×10^-8C and 6×10^-8C respectively.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/mulpoi.html
Remember, they asked for the potential (voltage) not the E field, so there is no need to do vectors, just add and subtract potential scalars.
To find the electric potential at the center of the square, you can use the principle of superposition. The electric potential at a point due to multiple point charges is the algebraic sum of the electric potentials due to each individual charge.
The electric potential at a point due to a point charge q is given by the equation:
V = k * q / r
where V is the electric potential, k is the electrostatic constant (= 9 × 10^9 Nm^2/C^2), q is the charge, and r is the distance between the charge and the point.
In this case, we have four charges at the corners of the square. Let's label them as q1, q2, q3, and q4, with values 3×10^-8C, -3×10^-8C, -5×10^-8C, and 6×10^-8C, respectively.
To find the electric potential at the center of the square, you need to calculate the electric potential due to each charge individually and then sum them up.
1. Calculate the distance between the center of the square and each corner. Since it's a square with a side length of 1m, the distance between the center and each corner is (1/√2)m.
2. Calculate the electric potential due to each charge using the formula V = k * q / r.
For q1:
V1 = (9 × 10^9 Nm^2/C^2) * (3 × 10^-8C) / (1/√2)m
For q2:
V2 = (9 × 10^9 Nm^2/C^2) * (-3 × 10^-8C) / (1/√2)m
For q3:
V3 = (9 × 10^9 Nm^2/C^2) * (-5 × 10^-8C) / (1/√2)m
For q4:
V4 = (9 × 10^9 Nm^2/C^2) * (6 × 10^-8C) / (1/√2)m
3. Sum up the individual electric potentials to get the total electric potential at the center of the square:
V_total = V1 + V2 + V3 + V4
Now, you can calculate this expression using a calculator, and you will find the electric potential at the center of the square.
I got 127.26 C-m
Please check the answer is correct or not
distance from center to each charge = (1/2) of diagonal = (1/2)sqrt(2) = .707 meter
so k/r for each charge = 1.27*10^10
so
V = 1.27*10^10 [ 0 + 6*10^-8 - 5*10^-8 ] note the first two cancel
= 1.27 *10^2 = 127 volts, agree