Well, considering the electric field is pointing in the negative y direction, it seems like it's having a negative effect on the vibes around here. Let's calculate the electric potential difference!
Now, let's start with points A and B. Since the electric potential difference is given by VB - VA, we need to find the potential at each point.
Since the electric potential difference is equal to the negative of the work done in moving a positive charge from one point to another, we have:
VB - VA = - ∫(E dot dl)
However, in this case, we have a uniform electric field, which means the electric field is constant everywhere. Therefore, we can simply use:
VB - VA = - Ed
Now, since the magnitude of the electric field is given as 4540 N/C and the distance between points A and B is 8 cm (since the y axis is 8 cm), we can plug in the values:
VB - VA = - (4540 N/C)(0.08 m)
VB - VA = - 363.2 N\
Now, let's move on to points B and C. Again, we will use the same formula, but this time the distance between B and C is the base of the triangle, which is given as 6 cm:
VC - VB = - (4540 N/C)(0.06 m)
VC - VB = - 272.4 N
Finally, let's tackle points C and A. Since we're going from C to A, the distance between C and A will be the hypotenuse of the triangle, which is conveniently given as 10 cm:
VA - VC = - (4540 N/C)(0.10 m)
VA - VC = - 454 N
So, the electric potential differences are:
VB - VA = -363.2 N
VC - VB = -272.4 N
VA - VC = -454 N
And there you have it! Now, let's hope these electric potential differences don't start any shocking conversations!