Question

Magnitude of electric field only on the x-coordinate as `vec(E)=20/x^(2) hat(i) V//m`. Find
(i) The potential difference between two points A (5m, 0) and B (10m, 0).
(ii) Potential at `x = 5` if V at `oo` is 10 volt.
(iii) In part (i), does the potential difference between a and B depend on whether the potential at `oo` is 10 volt or something else.

Answer 1

Given, `vec(E)=20/x^(2) hat(i) V//m`
We know that : `intdV=-int vec(E).vec(dr)" "implies" "underset(V_(1))overset(V_(2))(int)dV=-underset(x_(1))overset(x_(2))(int) 20/x^(2) dx`
`:.` Potential difference, `DeltaV=20/x|_(x_(1))^(x_(2))" "implies" "V_(2)-V_(1)=20/x_(2)-20/x_(1)`
(i) Potential difference between point A and B `(DeltaV" for A to B")`
`V_(B)-V_(A)=20/10-20/5=-2` volt
(ii) `DeltaV` for `x=oo` to `x=5`
`V_(5)-V_(oo)=20/5-20/oo" ":." "V_(5)=10+4=14` volt
(iii) Potential difference between two point does not depend on reference value of potential. So, the potential difference between a and B does not depend on whether the potential at `oo` is 10 volt ot something else.