Why Is the Equipotential Line Tangent to the Thick Black Line?

[yitriana]

Homework Statement

Find the points where the equipotential line is tangent to the thick black line

Homework Equations

The Attempt at a Solution

I thought that it was A, G and K, because there, the electric field is horizontal and thus perpendicular to the black line and electric field is always perpendicular to equipotential line. However, I am getting the answer wrong.

How do I approach this problem?

 

[thaer_dude]

A part of the problem is missing. A diagram most likely.

 

[kerimek]

It is important to first clarify the terms being used in this problem. An electric field is a vector field that describes the direction and strength of the electric force at any given point in space. Equipotential lines, on the other hand, are imaginary lines that connect points with equal electric potential. In other words, the electric field is perpendicular to the equipotential lines, not the other way around.

To solve this problem, we need to consider the relationship between the electric field and equipotential lines. Since the electric field is always perpendicular to equipotential lines, the tangent line at any point on an equipotential line will also be perpendicular to the electric field. This means that the points where the equipotential line is tangent to the thick black line will also be points where the electric field is perpendicular to the thick black line.

To find these points, we can use the fact that the electric field is given by the gradient of the electric potential. This means that the electric field will be perpendicular to the equipotential lines when the gradient of the electric potential is parallel to the thick black line. In other words, the points where the equipotential line is tangent to the thick black line will be the points where the gradient of the electric potential is parallel to the thick black line.

To find these points, we can use the concept of partial derivatives. We can take the partial derivative of the electric potential with respect to x and set it equal to zero to find the points where the gradient is parallel to the x-axis. Similarly, we can take the partial derivative with respect to y and set it equal to zero to find the points where the gradient is parallel to the y-axis. The intersection of these points will give us the desired points where the equipotential line is tangent to the thick black line.

In summary, to find the points where the equipotential line is tangent to the thick black line, we need to find the points where the gradient of the electric potential is parallel to the thick black line. This can be done by taking partial derivatives and finding the intersection of the resulting points.