A proton moves in a constant electric field from point A to point B. The magnitude of the electric field is 6.4 × 10^4 N/C; and it is directed as shown in the drawing, the direction opposite to the motion of the proton. If the distance from point A to point B is 0.50 m, what is the change in the proton's electric potential energy, EPEB – EPEA?
6.4×10^4 N/C x 0.50 m * 1.60*10^-19 C
(Joules)
EPE increases going from A to B (against the field force)
Thanks for the help, but I don't quite understand why you chose to multiply everything together.
To calculate the change in the proton's electric potential energy (EPE), we can use the formula:
ΔEPE = q * ΔV
Where:
ΔEPE is the change in the electric potential energy
q is the charge of the proton
ΔV is the change in the electric potential (difference in voltage)
Given that the distance from point A to point B is 0.50 m and the electric field magnitude is 6.4 × 10^4 N/C (directed opposite to the proton's motion), we can determine the change in voltage (ΔV) using the formula:
ΔV = -E * d
Where:
ΔV is the change in voltage
E is the magnitude of the electric field
d is the distance
Plugging in the values, we have:
ΔV = - (6.4 × 10^4 N/C) * (0.50 m)
= -3.2 × 10^4 V
Since the proton has a positive charge of +e, where e is the elementary charge, we can substitute the values into the formula for ΔEPE:
ΔEPE = q * ΔV
= (+e) * (-3.2 × 10^4 V)
= -3.2 × 10^4 eV
Therefore, the change in the proton's electric potential energy (EPEB – EPEA) is -3.2 × 10^4 eV.
To find the change in the proton's electric potential energy (EPE), we need to calculate the EPE at both point A and point B and then subtract the value at A from the value at B.
The formula to calculate the electric potential energy (EPE) is:
EPE = q * ΔV
Where:
- q represents the charge of the proton
- ΔV represents the change in electric potential
To find the change in electric potential (ΔV), we can use the formula:
ΔV = E / d
Where:
- E represents the magnitude of the electric field
- d represents the distance between the two points
Now let's calculate the change in the proton's electric potential energy step by step:
1. Calculate the change in electric potential (ΔV):
ΔV = E / d
= (6.4 × 10^4 N/C) / (0.50 m)
= 1.28 × 10^5 V
2. Calculate the charge of the proton (q):
The charge of a proton is typically given as +1.602 × 10^-19 C.
3. Calculate the EPE at point A (EPEA):
EPEA = q * ΔV
= (+1.602 × 10^-19 C) * (1.28 × 10^5 V)
≈ 2.05 × 10^-14 J (Joules)
4. Calculate the EPE at point B (EPEB):
EPEB = q * ΔV
= (+1.602 × 10^-19 C) * (-1.28 × 10^5 V) [opposite direction]
= -2.05 × 10^-14 J (Joules)
5. Calculate the change in the proton's electric potential energy (EPEB - EPEA):
EPEB - EPEA = (-2.05 × 10^-14 J) - (2.05 × 10^-14 J)
= -4.10 × 10^-14 J (Joules)
Therefore, the change in the proton's electric potential energy, EPEB – EPEA, is approximately -4.10 × 10^-14 J (Joules).