Three positive particles of charges 1 μC, 2 μC, 3 μC, and 4 μC, are located at the corners of a square of side 1 cm. Calculate the potential in the center of the square, taking V = 0 at a great distance.
φ=φ1+φ2+φ3+φ4= k{(q1/r)+ (q2/r)+ (q3/r)+ (q4/r)}
a=0.01 m, r=a√2/2=0.007 m
k=9•10^9 F/m
φ= (9•10^9•10^-6/0.007) •(1+2+3+4)=1.29•10^7 V
To calculate the potential in the center of the square, we can use the principle of superposition. The potential at a point due to multiple charges is the algebraic sum of the potentials at that point due to each individual charge.
Let's break down the problem into smaller steps:
1. Calculate the potential due to each individual charge at the center of the square:
The potential due to a point charge at a distance 'r' is given by the equation V = kq/r, where V is the potential, k is the Coulomb constant (k = 9 × 10^9 Nm^2/C^2), and q is the charge.
Using this equation, we can calculate the potential due to each charge at the center of the square:
- The potential due to the 1 μC charge is V1 = k(1 μC) / r1, where r1 is the distance between the 1 μC charge and the center of the square.
- The potential due to the 2 μC charge is V2 = k(2 μC) / r2, where r2 is the distance between the 2 μC charge and the center of the square.
- The potential due to the 3 μC charge is V3 = k(3 μC) / r3, where r3 is the distance between the 3 μC charge and the center of the square.
- The potential due to the 4 μC charge is V4 = k(4 μC) / r4, where r4 is the distance between the 4 μC charge and the center of the square.
2. Calculate the net potential at the center of the square:
Next, we need to compute the sum of the potentials due to each individual charge. Since potential is a scalar quantity, we can simply add them up:
Vnet = V1 + V2 + V3 + V4
3. Calculate the final potential at the center of the square:
Finally, once we have the net potential due to all the charges, we can find the final potential in the center of the square by subtracting the potential at a great distance (V = 0) from the net potential:
Vfinal = Vnet - V(great distance)
Since the problem statement mentions that V = 0 at a great distance, we can simply ignore the second term and write the final potential as:
Vfinal = Vnet
By plugging in the values mentioned in the problem and performing the calculations, you will be able to find the potential at the center of the square.