question_answer

The electric potential in a region is given by\[V(x,\text{ }y,\text{ }z)\] =\[a{{x}^{2}}+a{{y}^{2}}+ab{{z}^{2}}\], 'a' is a positive constant of appropriate dimensions and b, a positive constant such that V is volts when x, y, z are in m. Let\[b=2\]. The work done by the electric field when a point charge\[+4\mu C\]moves from the point (0, 0, 0, 1m) to the origin is\[50\mu J\]. The radius of the circle of the equipotential curve corresponding to \[V=6250\text{ }volts\]and \[z=\sqrt{2}\]m is \[\alpha \]m. Find\[{{\alpha }^{2}}\].

Answer:

3.00