Physical meaning of the equation E = - del V

[Flying_Dutchman]

The gradient of a function gives a vector perpendicular to it's surface. So the equation reads electric field is the negative of the vector perpendicular to the equipotential surface. I know electric field and understand potential but I can't physically make sense for the above sentence how LHS is equal to RHS.
Hope anyone will answer .Thank you !

 

[Nugatory]

It’s a definition. You may be able to visualize the relationship if you consider a standard topographical map as a two-dimensional analogy: the gradient of the altitude is a vector perpendicular to the contour lines of equal height, and it points in the direction that a ball at that point will naturally roll.

 

[Dale]

The gradient does not just give any random vector which is perpendicular to the equipotential surface, but specifically the vector whose magnitude is equal to the rate of change of the function in that direction. So perhaps it is a little easier to understand:

The electric field is a vector whose direction is normal to the equipotential surface and whose signed magnitude is equal to the negative rate of change of the potential in that direction.

 

[Herman Trivilino]

I know electric field and understand potential but I can't physically make sense for the above sentence how LHS is equal to RHS.

Start by looking at an ideal parallel plate capacitor. What is the relationship between the voltage difference between the plates and the electric field between the plates?

 

[Herman Trivilino]

It’s a definition.

Not in the way it's usually presented in introductory college-level physics textbooks and courses. Field is defined as force per unit charge and potential is defined as potential energy per unit charge. From there the relationship between field and potential is derived.

 

[ZapperZ]

The gradient of a function gives a vector perpendicular to it's surface. So the equation reads electric field is the negative of the vector perpendicular to the equipotential surface. I know electric field and understand potential but I can't physically make sense for the above sentence how LHS is equal to RHS.
Hope anyone will answer .Thank u !

I often do not understand this type of question, because you essentially have accepted this in another form. Let me prove it to you.

Multiple both sides by a charge q that is in this E and V fields, i.e. you get

qE = - ∇qV

which is nothing more than

F = - ∇U

where F is the force acting on the charge q, and U is the potential energy. This is the general relationship between the force and the potential energy, i.e. force is the gradient of potential energy field.

Now, do you have a problem having an understanding or a visual picture of this, because you have accepted this already when it is applied to kinematics, such as force in a gravitational field. There is nothing different here, with the mathematics being identical to each other.

Zz.