A potential charge of magnitude 2.0uC is moved between two points X and Y Point X is at a potential of 6.0V and Point Y is at a potential of 9.0 V Find the gain in potential energy of Point charge
0.20 mew J
Well, well, well! It looks like our point charge is going on a journey from X to Y, collecting potential energy along the way. Let's calculate that gain in potential energy and hope it doesn't develop a big head!
The gain in potential energy can be calculated using the equation:
ΔU = q * ΔV
Where:
ΔU is the gain in potential energy
q is the charge
ΔV is the change in potential
Now, we are told that the potential at X is 6.0V and the potential at Y is 9.0V. So, the change in potential, ΔV, is:
ΔV = VY - VX
ΔV = 9.0V - 6.0V
ΔV = 3.0V
Now, we don't know the exact value of the charge q, but we do know it's magnitude, which is 2.0uC. The "u" here stands for micro, which means 10^-6. So, 2.0uC is 2.0 x 10^-6 C.
Now, let's put it all together and calculate the gain in potential energy:
ΔU = q * ΔV
ΔU = (2.0 x 10^-6 C) * (3.0V)
ΔU = 6.0 x 10^-6 J
So, our point charge has gained a potential energy of 6.0 x 10^-6 J during its journey from X to Y. Phew, that's quite a gain! I hope it doesn't become too charged up with this newfound energy!
To find the gain in potential energy of the point charge, we can use the formula:
ΔPE = q ΔV
Where:
ΔPE is the gain in potential energy
q is the charge
ΔV is the change in potential
Given:
q = 2.0 uC = 2.0 × 10^-6 C (convert from microCoulombs to Coulombs)
ΔV = 9.0 V - 6.0 V = 3.0 V
Substituting the values into the formula, we have:
ΔPE = (2.0 × 10^-6 C) × (3.0 V)
= 6.0 × 10^-6 J
Therefore, the gain in potential energy of the point charge is 6.0 × 10^-6 Joules.
To find the gain in potential energy of the point charge, we can use the equation:
ΔPE = q * ΔV
where:
ΔPE is the change in potential energy,
q is the magnitude of the charge, and
ΔV is the potential difference.
In this case, the magnitude of the charge q is given as 2.0 μC (microcoulombs).
The potential difference ΔV can be found by subtracting the initial potential (Point X) from the final potential (Point Y):
ΔV = VY - VX
ΔV = 9.0 V - 6.0 V
ΔV = 3.0 V
Now, we can calculate the gain in potential energy:
ΔPE = q * ΔV
ΔPE = (2.0 μC) * (3.0 V)
To simplify the calculation, we need to convert 2.0 μC to coulombs:
1 μC = 10^-6 C
2.0 μC = 2.0 * 10^-6 C
ΔPE = (2.0 * 10^-6 C) * (3.0 V)
ΔPE = 6.0 * 10^-6 J
Therefore, the gain in potential energy of the point charge is 6.0 * 10^-6 joules (J).