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Miraj Kayastha

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- Thread starter Miraj Kayastha
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In summary, the electric field strength is always equal to the negative potential gradient. This relationship is true in any circumstance and there are no exceptions. The equation for finding the electric field strength between two parallel plates is E = V/d, which is an equation for the magnitude. However, when considering the electric field as a vector, a negative sign is attached to indicate the direction towards lower potential. In cases involving induction with time-varying magnetic fields, there is an additional term in the equation for electric field, -dA/dt, which accounts for the non-conservative portion of the total field. The negative sign in the equation for electric potential is a sign convention, chosen so that bringing a charge from infinity to a point in space

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Miraj Kayastha

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FOIWATER

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Miraj Kayastha

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Isn't the formula for finding the electric field strength between two parallel plates E =V/d

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FOIWATER

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In fact you need it in that case. The E field increases towards lower potential (means a positive direction is pointing in the direction of E, that is, to a lower potential). In V=-Ed, a negative direction (corresponding to moving towards a positive potential) will give you a positive result for V. if you are moving away from the higher potential, a positive direction, the potential is lower. So I believe it is just a matter of calculating magnitudes vs. considering it as a vector.

If I have misled you someone will clarify it for us both. I am no expert but I just did an electromagnetics class

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Miraj Kayastha

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why is there a negative sign in the equation E = -V/d?

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jtbell

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cabraham

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This E field is not the gradient of the scalar electric potential V. It is as follows:

Any e/m fields text will elaborate.

Claude

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Dale

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So the sign of ##\nabla V## is always negative, never positive, but there is an additional term besides just the negative gradient of the potential. This is what cabraham is talking about.

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cabraham

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DaleSpam said:

So the sign of ##\nabla V## is always negative, never positive, but there is an additional term besides just the negative gradient of the potential. This is what cabraham is talking about.

Yes of course. The 1st term:

-grad V

refers to the conservative portion of the total E field. The 2nd term:

-dA/dt

refers to the non-conservative portion of said E field. An example would be where a loop is immersed into a time changing magnetic field. The loop is circular, where each half of the loop is a different resistivity material semicircular in shape. Of course the 2 semicircular loops are in series so they have the same current, but the voltage across each half must be equal as they are also in parallel. This condition is met by virtue of charge layer accumulation at the 2 boundaries between the media. The electrons moving around the loop feel the Lorentz force from both the time varying B field as well as the static charges accumulated at the boundaries.

The result is that there are 2 E fields, one from induction, non-conservative, given by the 1st term above, and a 2nd, conservative, per 2nd term above. Interesting stuff this is.

Claude

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Miraj Kayastha said:

This is a very strange question. It is as if you are asking if this description is negotiable.

Zz.

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Henriamaa

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It is a sign convention. Remember that [itex] V=- \int E.dl [/itex] the minus sign is place there so that when we bring a charge from infinity (where the potential is defined as 0) and place it at some point in space we arrive at some positive value for V and therefore the work we have done is positive

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sophiecentaur

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Electric potential is a measure of the amount of work needed to move a unit charge from one point to another in an electric field. It is measured in volts (V) and is a scalar quantity.

The electric potential at a point is directly proportional to the electric field at that point. This means that if the electric field is stronger, the electric potential will be higher, and vice versa. The relationship is given by the equation: V = Ed, where V is the electric potential, E is the electric field, and d is the distance between the two points.

Negative electric potential gradient is a measure of the decrease in electric potential per unit distance. It indicates that the electric potential is decreasing in the direction of the electric field. In other words, the electric field is doing work on the charge and decreasing its potential energy.

Negative electric potential gradient is represented by a downward sloping line on a graph of electric potential versus distance. This indicates that as the distance increases, the electric potential decreases.

The negative electric potential gradient is important because it helps us understand the behavior of electric fields. It shows us that electric fields have a direction and can do work on charges, leading to changes in their potential energy. It also allows us to calculate the electric field strength at a given point using the equation E = -dV/dx, where E is the electric field, V is the electric potential, and x is the distance along the field direction.

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