If Electric field in a region is given by E=x2^i+y^j+^k. What is the potential of the point (1,2,3) given the potential of the origin is 10V?
143V
Since we know E=−dVdr,
To find V, we use the inverse operation of differentiation, which is integration.
V=−∫r2r1Edr
So in a Cartesian coordinate system, the above equations become
E=−(∂V∂x^i+∂V∂y^j+∂V∂z^k)
Where, ∂∂xrepresents the partial derivative w.r.t x alone keeping variables y and z constant.
So for the above question,
V=−(∫10x2+∫20y+∫301)
V=−(x33|0 1+y22|0 2+z|0 3)
V=−(13+2+3)
V=−163V
Remember that this is only the potential difference between points (1,2,3) and (0,0,0).
Since the potential at (0,0,0) is 10 V,
The answer we are looking for is V=10−163=143.