Question

An electric field of 20n/c exist along the direction of 3i-4j+5k in space . calculate potential difference betwwen

Answer 1

Your question is incomplete .
A complete question is -------> An electric field of 20 N/C exist along the direction 3iˆ−4jˆ+5kˆ in space. Calculate the potential difference VA - VB where the points A and B are given by A = (0, 0, 0); B = (4, 2, 1)?
electic field exists along the direction of r = 3i - 4j + 5k in space.
so, unit vector of E = unit vector r
E/|E| = r/|r|
E = |E|/|r| r
= 20/√50 (3i - 4j + 5k) [ ∵ |r| = √(3² + (-4)² + 5²) = √50 ]
= 2√2(3i - 4j + 5k)
= 6√2i - 8√2j + 10√2k
Now , separation vector = AB = (4 -0)I + (2 - 0)j + (1- 0)k
AB = 4i + 2j + 1k

Potential difference is given by
∆V = E.AB
= (6√2i - 8√2j + 10√2k).(4i +2j + k)
= 24√2 - 16√2 + 10√2
=18√2 V

Hence, answer is 18√2 V