A uniform electric field of magnitude 320 V/m is directed in the negative y direction. The coordinates of point A are (-0.300, -0.450) m, and those of point B are (0.650, 0.300) m. Calculate the electric potential difference VB − VA.
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To calculate the electric potential difference (VB - VA) between point B and point A, we need to consider the effect of the electric field on each point. The electric potential at a point in an electric field is given by the formula:
V = Ed
where V is the electric potential, E is the magnitude of the electric field, and d is the displacement vector between the point and a reference point.
Here's how we can find the electric potential at point A and point B:
1. Determine the displacement vector from each point to a reference point. Let's assume the reference point is at the origin (0, 0).
For point A:
dA = (-0.300, -0.450) m - (0, 0) m = (-0.300, -0.450) m
For point B:
dB = (0.650, 0.300) m - (0, 0) m = (0.650, 0.300) m
2. Calculate the electric potential at each point using the formula V = Ed.
For point A:
VA = 320 V/m * (-0.300, -0.450) m
To calculate VA, we multiply the magnitude of the electric field (320 V/m) by the displacement vector (-0.300, -0.450) m.
VA = (320 V/m) * (-0.300, -0.450) m
VA = (-96 V, -144 V)
For point B:
VB = 320 V/m * (0.650, 0.300) m
To calculate VB, we multiply the magnitude of the electric field (320 V/m) by the displacement vector (0.650, 0.300) m.
VB = (320 V/m) * (0.650, 0.300) m
VB = (208 V, 96 V)
3. Finally, calculate the electric potential difference (VB - VA) by subtracting the components:
VB - VA = (208 V, 96 V) - (-96 V, -144 V)
VB - VA = (208 V + 96 V, 96 V + 144 V)
VB - VA = (304 V, 240 V)
So, the electric potential difference (VB - VA) between point B and point A is (304 V, 240 V).