Equipotential line and electric field

[Saitama]

Homework Statement

The equation of an equipotential line in an electric field is y=2x, then the electric field strength vector at (1,2) may be
a)4i+3j
b)4i+8j
c)8i+4j
d)-8i+4j

Homework Equations

The Attempt at a Solution

Since its an equipotential line, the electric field vector should perpendicular to this line. Therefore, the slope of line perpendicular to y=2x is -1/2. The equation should be y=\frac{-1}{2}x+k, where k is any constant. Now i am stuck, can somebody help me proceed in the right direction?

 

[Infinitum]

You cannot find the exact vector, as there can be many answers satisfying the given condition. But, you sure can check the options to see which of them would give you a vector perpendicular to y=2x

I believe the options were specifically made that way so that you can get the answer.

 

[Saitama]

You cannot find the exact vector, as there can be many answers satisfying the given condition. But, you sure can check the options to see which of them would give you a vector perpendicular to y=2x

I believe the options were specifically made that way so that you can get the answer.

Yes, many answers are possible.
How can i check that the vector is perpendicular to line y=2x?

 

[Infinitum]

Yes, many answers are possible.
How can i check that the vector is perpendicular to line y=2x?

Check the slopes of the vectors!

 

[Saitama]

Check the slopes of the vectors!

Lol, then the answer is d), its slope is -1/2.
But then what's the use of (1,2)?

EDIT: Got it why the points are given. :)

 

[Infinitum]

Lol, then the answer is d), its slope is -1/2.
But then what's the use of (1,2)?

EDIT: Got it why the points are given. :)

Good going!