A region in space has a constant electric field 6x103i N/C. What is the potentia

Question

A region in space has a constant electric field 6x103i N/C. What is the potential difference along each of the following paths? (a) From the origin to (3,3) m, first moving along the x-axis from (0,0) m to (3,0) m, then moving in the y-direction from (3,0) m to (3,3) m (b) From the origin to (3,3) m, moving along a 45° angle (i.e. straight-line from (0,0) m to (3,3) m) (c) From the origin along a square that goes 3 m to the right to (3,0) m, then 3 m up to (3,3) m, then 3 m to the left to (0,3) m, then three meters down to (0,0) m, eventually returning back to the origin.

Explanation / Answer

Given

the region of constant electric field is E = 6000 i N/C

we know that the potential is a scalar quantity which depends on the position of the point inside the electric field  

so what ever the path choosed to reach the final point the potential is constant between the two points

we have the relation between the electric field and potential difference between two points is  

V = E*d

V = E*sqrt((x2-x1)^2 +(y2-y1)^2)

V = 6000 sqrt((3-0)^2+(3-0)^2) V

v = 25455.844 V

b) we can get the same potential difference at (3,3) in the direction of 45 degrees with x axis  

because the potential is not path dependant it is path independent quantity like gravitational potential energy

c) the potential is zero upon reaching the same point  

V = E*d = E*0 = 0 V

the potential difference is zero

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