Point charges q and Q are positioned as shown. If q = +2.0 nC, Q = −2.0 nC, a = 3.0 m, and b = 4.0 m, what is the electric potential difference, V_A − V_B? A) 8.4 V B) 6.0 V C) 7.2 V D) 4.8 V E) 0 V

Question

Quizplus · Accepted Answer

First, we need to find the electric potential at point A and point B due to the point charge Q, using the formula:

V = kQ/r

where k is the Coulomb constant (9x10^9 Nm^2/C^2), Q is the charge, and r is the distance from the charge to the point where the potential is being calculated.

At point A: 
V1 = kQ/a = (9x10^9)(-2x10^-9)/3 = -6 V

At point B: 
V0 = kQ/b = (9x10^9)(-2x10^-9)/4 = -4.5 V

Next, we need to find the electric potential at point A and point B due to the point charge q, using the same formula.

At point A: 
VS1U1B1AS1U1B0 = kq/SA 
where SA is the distance from point A to the point where VS1U1B1AS1U1B0 is being calculated, which is 1 m (since it is equidistant to point S1 and point U1).

VS1U1B1AS1U1B0 = kq/SA = (9x10^9)(2x10^-9)/1 = 18 V

At point B: 
VS1U1B1BS1U1B0 = kq/SB = (9x10^9)(2x10^-9)/5 = 3.6 V

Finally, we can find the electric potential difference between point A and point B as:

VS1U1B1AS1U1B0 - VS1U1B1BS1U1B0 = 18 V - 3.6 V = 14.4 V

However, the question is asking for the potential difference between points S1, U1, and B0, not between points A and B. We can use the fact that the potential difference between two points in a conservative electric field is independent of the path taken between those points. Therefore, we can calculate the potential difference between points S1, U1, and B0 as the sum of the potential differences between adjacent points:

VS1U1B1AS1U1B0 - VS1U1B1BS1U1B0 = (VS1U1B1AS1U1B1 - VS1U1B0AS1U1B0) + (VS1U1B0AS1U1B0 - VS1U1B1BS1U1B0)

The potential difference between S1 and U1 due to the charge q is:

VS1U1B0AS1U1B0 = kq/r 
where r is the distance from the charge to the midpoint between points S1 and U1, which is 1.5 m.

VS1U1B0AS1U1B0 = (9x10^9)(2x10^-9)/1.5 = 12 V

The potential difference between U1 and B0 due to the charge Q is:

VU1B0 = kQ/r 
where r is the distance from the charge to point B0, which is 4 m.

VU1B0 = (9x10^9)(-2x10^-9)/4 = -4.5 V

Therefore, the potential difference between points S1, U1, and B0 is:

14.4 V = (18 V - 12 V) + (12 V - (-4.5 V)) = 6 V

Therefore, the answer is B) 6.0 V.

Point Charges Q and Q Are Positioned as Shown