Electric field & Potential?

Question

We know that electric field can be written as a NEGATIVE gradient of a scalar potential.....why is that NEGATIVE there, what is it physical significance.

Answer 1

Negative just indicates that the direction of the electric force on a positively charged particle (i.e., the direction of the electric field) is in the direction of decreasing potential. That is, a positive electric charge will experience a force in the direction from greater potential to lesser potential. Here's why it is negative.

The scalar potential is defined as zero at infinity. At any point other than infinity, it is the amount of work required to move a positively charged particle from infinity to a particular location. Positive potential means that work has to be done on the particle. Therefore, the force must have been directed against that positively charged particle. You had to "push against the field" to get that particle from 0 potential at infinity to the positive potential.

So, if the positively charged particle were released from rest at a point where the field was positive, it would want to move to lower potential - the field would push on it. Therefore, the direction of force - i.e., the direction of the field - is toward lower potential.

Imagine the scalar potential analogous to the gravitational potential. The gravitational potential is like a measure of elevation - the higher the potential, the higher the "hill." Just as a ball (i.e., positive charge) released from rest rolls down a hill from higher potential to lower potential, so too does a positive charge experience a force in the direction from higher electric potential to lower electric potential.

Answer 2

When we calculate electric potential at a distant place from a charged body, we normaly take the body as a positive point charge concentrated at the center of the body( I ma not talking about potential inside the body or variable charge distribition in the body). Electric field lines are coming out from the body are normal to the spherical surface drawn keeping the charge at the centre of the sphere. As we go farther surface number of lines /unit area decreases . Therefore as we go farther potential decreases i.e work done on the test charge is negative. that is the reason of negative sign.

Answer 3

Electric field E= - dV /dr As potential is constant dV / dr =zero Hence electric field is zero in a region where electric potential is constant. For example, inside a hollow charged matallic sphere, THE ELECTRIC FIELD IS ZERO BUT THE POTENTIAL INSIDE IS CONSTANT and equal to potential on the suface of charged sphere

Answer 4

its written negative gradient to make the whole term posative

Answer 5

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