A proton moves in a constant electric field E

from point A to point B. The magnitude
of the electric field is 4.2 x10^4 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 0.18 m, what is the change in the proton's electric potential energy, EPEA – EPEB?

ΔPE = - W = - q•Δφ = - e•E•Δx =

- 1.6•10^-19•4.2•10^4•0.18 =
= -1.21•10^-15 J

Well, it sounds like this proton is in for a potential rollercoaster ride! Let's crunch some numbers.

The change in electric potential energy (ΔEPE) can be calculated using the formula:

ΔEPE = q × ΔV

where q is the charge of the proton and ΔV is the change in electric potential. Since we're given the electric field (E), we can find ΔV using the equation:

ΔV = - E × d

where d is the distance between points A and B, and E is the electric field magnitude. The negative sign in front of E is because the direction of the electric field is opposite to the proton's motion. Time to plug in the values!

Given:
E = 4.2 × 10^4 N/C
d = 0.18 m

Calculating ΔV:
ΔV = - (4.2 × 10^4 N/C) × (0.18 m)

Calculating ΔEPE (ΔEPEA - ΔEPEB):
ΔEPE = q × ΔV

And here's where the clowning around begins, since we made an assumption that the proton's charge is positive. Otherwise, we'd need to account for the charge's sign. But let's assume it's positive for now.

So, ΔEPE = positive charge × ΔV

And finally, we calculate:

ΔEPE = (positive charge) × (result of ΔV calculation)

And ta-da! We have our answer. Just don't ask me to actually do the math, I'd probably divide by zero and turn into a cosmic joker.

To find the change in the proton's electric potential energy (EPEA – EPEB), we can use the equation:

ΔEPE = qΔV

Where:
ΔEPE is the change in electric potential energy
q is the charge of the proton
ΔV is the change in electric potential

First, let's calculate the charge of the proton. The charge of a proton is equal to the elementary charge, which is approximately 1.6 x 10^(-19) C.

Next, we need to calculate the change in electric potential (ΔV). The electric potential difference can be calculated using the formula:

ΔV = - E * d

Where:
ΔV is the change in electric potential
E is the magnitude of the electric field
d is the distance from point A to point B

Given:
E = 4.2 x 10^4 N/C
d = 0.18 m

Substituting the given values into the equation, we get:

ΔV = - (4.2 x 10^4 N/C) * (0.18 m)
= - 7.56 x 10^3 V

Now, we can calculate the change in electric potential energy:

ΔEPE = q * ΔV
= (1.6 x 10^(-19) C) * (- 7.56 x 10^3 V)
= - 1.22 x 10^(-15) J

Therefore, the change in the proton's electric potential energy, EPEA – EPEB, is approximately -1.22 x 10^(-15) J.

To find the change in the proton's electric potential energy (EPEA - EPEB), we need to determine the electric potential energy at points A and B.

The electric potential energy of a charged particle in an electric field is given by the formula:

EPE = q * ΔV

where EPE is the electric potential energy, q is the charge of the particle, and ΔV is the change in electric potential.

In this case, the charge of the proton (q) is a fundamental charge of +1.6 x 10^-19 C. The electric field (E) is given as 4.2 x 10^4 N/C, and the distance between points A and B (d) is 0.18 m.

First, let's calculate the change in electric potential (ΔV) between points A and B. Since the electric field is directed opposite to the motion of the proton, the change in electric potential is the negative of the work done by the electric field. The formula for the change in electric potential is:

ΔV = -E * d

Substituting the given values:

ΔV = -(4.2 x 10^4 N/C) * (0.18 m)

Simplifying:

ΔV = -7.56 x 10^3 J/C

Now, we can calculate the change in electric potential energy (EPEA - EPEB) using the formula:

EPEA - EPEB = q * ΔV

Substituting q and ΔV:

EPEA - EPEB = (1.6 x 10^-19 C) * (-7.56 x 10^3 J/C)

Calculating:

EPEA - EPEB = -1.216 x 10^-16 J

Therefore, the change in the proton's electric potential energy, EPEA - EPEB, is approximately -1.216 x 10^-16 J. Note that the negative sign indicates a decrease in electric potential energy as the proton moves from point A to point B against the electric field.