Question

The equation of an equipotential line in an electric field is y = 2x, then the electric field vector at (1, 2) may be

Answer 1

If you visualize equipotential lines as contours on a map, such type of problems are in fact very easy to solve. Take example of any topographic map. You may observe that the descent and ascent is always perpendicular to the direction of contour line.
Similarly, the direction of electric field is always perpendicular to the contour line and it points towards the descent.
Your equipotential line is $y=2x$ whose slope $m=2$.
Use $m_{\perp}=-\dfrac{1}{m}=-\dfrac{1}{2}$
Therefore, the direction of the electric field vector should be towards the line:$y=-\dfrac{1}{2}x or x+2y=0$.

Answer 2

Question

The equation of an equipotential line in an electric field is y=2x, then the electric field strength vector at (1,2) may be

Answer

Electric field is perpendicular to equipotential line

dy/dx= 2

m1=2

m1m2=-1

m2=-½

tan theata =-½

where θ is angle with x-axis.

tan theata = 4/-8=-½