In an electric field described by E = (20i+60j) V/m calculate the change in potential for a particle that moves from the origin to the coordinates (3,3)m
To calculate the change in potential for a particle moving in an electric field, we use the formula:
ΔV = -∫ E · dr
Here, ΔV represents the change in potential, E is the electric field vector, and dr is the displacement vector along the path.
In this case, we have the electric field E = (20i + 60j) V/m, and we want to calculate the change in potential for a particle that moves from the origin (0,0) to the coordinates (3,3)m.
To compute the change in potential, we need to integrate the dot product of the electric field and the displacement vector along the path from (0,0) to (3,3). Let's first calculate the displacement vector:
dr = dx i + dy j
where dx and dy are the changes in x and y coordinates, respectively.
In this case, dx = 3m - 0m = 3m and dy = 3m - 0m = 3m.
So, dr = 3i + 3j.
Now, let's calculate the dot product of the electric field and the displacement vector:
E · dr = (20i + 60j) · (3i + 3j)
= 20(3) + 60(3)
= 60 + 180
= 240 V
The dot product of the electric field and displacement vector is 240 V.
Finally, substitute this result into the formula to find the change in potential:
ΔV = -∫ E · dr
= -240 V
Therefore, the change in potential for the particle moving from the origin to the coordinates (3,3)m is -240 V.