Point X and Y are 30.0 mm and 58.0 mm away from a charge of +8.0 C.
a. How much work must be done in moving a +2.0 C charge from point Y to point X?
b. What is the potential difference between points X and Y?
c. Which point is at the higher potential?
the square shape is for mu.....
To solve these questions, we need to use Coulomb's Law and the definition of electric potential.
a. To calculate the work done in moving a charge from point Y to point X, we can use the formula for electric potential energy:
Electric Potential Energy (W) = Charge (q) * Potential Difference (V)
The potential difference between two points is the work done per unit charge in moving a charge from one point to another.
In this case, we are given the charge (+2.0 µC) and we need to find the potential difference. To find the potential difference, we need to calculate the electric potential at each point.
The electric potential (V) for a point around a charged object is given by:
Electric Potential (V) = k * (Q / r)
where k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), Q is the charge, and r is the distance from the charge.
With Q = +8.0 µC, r = 30.0 mm = 0.03 m, and r = 58.0 mm = 0.058 m, we can calculate the electric potentials at points X and Y.
Electric Potential at X (Vx) = k * (Q / rX)
Electric Potential at Y (Vy) = k * (Q / rY)
Substituting the given values, we get:
Vx = (8.99 x 10^9 Nm^2/C^2) * (8.0 x 10^-6 C) / 0.03 m
Vy = (8.99 x 10^9 Nm^2/C^2) * (8.0 x 10^-6 C) / 0.058 m
Calculate Vx and Vy to find the potentials at points X and Y.
Now, we know that the potential difference (V) between two points is given by the difference in electric potential (Vx - Vy).
V = Vx - Vy
Substitute the values of Vx and Vy and calculate V to find the potential difference between points X and Y.
Finally, using the formula for electric potential energy, we can calculate the work done (W) in moving the charge (+2.0 µC) from point Y to point X:
W = q * V
Substitute the values of q and V to calculate the work done.
b. The potential difference between points X and Y is the value calculated in part "a". Find V to find the answer.
c. The point with the higher potential is the point with the higher electric potential. Compare the values of Vx and Vy calculated above to determine which point has a higher electric potential. The point with the higher value is at the higher potential.
Please note: It is important to convert the given distances into meters (m) to be consistent with the SI unit used in Coulomb's Law and the formula for electric potential.
Potenial at each point: kQ/r
work= differencein potential* distance y to X.
difference in potential= PotentialY-PotentialX
The closer is the higher potential