Point charges Q1 ,Q2 , and Q3 reside on three corners of a square with sides of 1m ; the distance from Q2 to P3 is 2m (see diagram).
(a) What is the electric potential,V , at P1 ? (Normalize the potential to be zero at infinity and give your answers in Volts).
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What is V at P2 (in Volts)?
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What is V at P3 (in Volts)?
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(b) Are there points or surfaces in space (other than infinity) where V is zero?
(c) What is the electrostatic potential energy of the system? Express your answer in Joules.
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Please some one answer.
To calculate the electric potential at each point, we need to know the charges of the point charges Q1, Q2, and Q3. Please provide the charges of each point charge.
To find the electric potential at a point due to multiple point charges, we can use the formula:
V = k * (Q1 / r1 + Q2 / r2 + Q3 / r3)
where V is the electric potential, Q1, Q2, and Q3 are the charges, r1, r2, and r3 are the distances from the charges to the point, and k is the Coulomb's constant (k = 8.99 x 10^9 N m^2 / C^2).
(a) Electric potential at P1:
To find the electric potential at P1, we need to calculate the distances from Q1, Q2, and Q3 to P1. As P1 is on a corner of the square and the sides of the square are 1m, the distance from Q1 to P1 is the diagonal of the square, which can be calculated using the Pythagorean theorem:
r1 = √(1^2 + 1^2) = √2 m
Similarly, the distance from Q2 to P1 is the diagonal of the square plus the distance between Q2 and P3:
r2 = √(2^2 + 1^2) = √5 m
The distance from Q3 to P1 is simply the distance between P1 and P3:
r3 = 2m
Now, substitute the values into the formula to find the electric potential at P1:
V = k * (Q1 / r1 + Q2 / r2 + Q3 / r3)
(b) Electric potential at P2:
To find the electric potential at P2, we need to calculate the distances from Q1, Q2, and Q3 to P2. As P2 is on the midpoint of one of the sides of the square, the distance from Q1 to P2 is simply 1m. The distance from Q2 to P2 is the diagonal of the square minus the distance between Q2 and P3:
r2 = √(2^2 + 1^2) - 2m = √5 - 2 m
The distance from Q3 to P2 is the diagonal of the square minus the distance between Q3 and P3:
r3 = √(2^2 + 2^2) - 2m = 2√2 - 2 m
Now, substitute the values into the formula to find the electric potential at P2:
V = k * (Q1 / r1 + Q2 / r2 + Q3 / r3)
(c) Electric potential at P3:
To find the electric potential at P3, we need to calculate the distances from Q1, Q2, and Q3 to P3. As P3 is on one of the sides of the square, the distance from Q1 to P3 is 1m. The distance from Q2 to P3 is 2m, given in the question. The distance from Q3 to P3 is simply 0m.
Now, substitute the values into the formula to find the electric potential at P3:
V = k * (Q1 / r1 + Q2 / r2 + Q3 / r3)
(b) Yes, there are points or surfaces in space (other than infinity) where the electric potential V is zero. This occurs when the sum of the potential contributions from the charges at those points cancels out.
(c) The electrostatic potential energy of a system can be found using the formula:
U = k * (Q1 * Q2 / r12 + Q1 * Q3 / r13 + Q2 * Q3 / r23)
where U is the electrostatic potential energy, Q1, Q2, and Q3 are the charges, and r12, r13, and r23 are the distances between the charges.
Now, substitute the values into the formula to find the electrostatic potential energy of the system:
U = k * (Q1 * Q2 / r12 + Q1 * Q3 / r13 + Q2 * Q3 / r23)
Please provide the values of the charges (Q1, Q2, Q3) to calculate the potential energy.