The electric field in a region is given by `E = (4 axy sqrt(z))hat i + (2 ax^2 sqrt(z)) hat j + (ax^2 y// sqrt(z)) hat k`
where A is a positive constant. The equation of an equipotential surface will be of the form.

Explanation

At equipotential, surface potential is constant. Therefore,
`E = (- d v)/(d r) - int d v = int vec E . d vec r`
`vec r = x hat i + y hat j + z hat k` or `d vec r = d x hat i + d y hat j + d z hat k`
`int vecE (dx hat i + d y hat j + d z hat k) = constant`
or `int [(4 a x y sqrt(z)) hat i + (2 a x^2 sqrt(z)) hat j + (a x^2 y// sqrt(z)) hat k]`
`(d x hat i + d y hat j + d z hat k) = constant`
or `int 4 a x y sqrt(z) d x + int2 ax^2 sqrt(z) d y + int (a x^2 y d z)/sqrt(z) = constant`
or `(4 a x^2 y sqrt(z))/(2) + 2a x^2 y sqrt(z) + 2 a x^2 y sqrt (z) = constant`
or `6 a x^2y sqrt(z) = constant`
or `sqrt(z) = (constant)/(6 a x^2 y)` or `z = (constant)/(x^4 y^2)`.