Voltage difference, line integral

In summary, the conversation discusses an integral formula involving an electric field and a direction vector, and the confusion surrounding the direction of the vector and the negative sign in the formula. The direction of the vector is arbitrary and the potential difference in an electric field may depend on the path taken. There may also be a misplaced minus sign in the formula.
  • #1
kougou
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0

Homework Statement

I don't understand the follow formula of the integral :

Integral of ( E dot dL) from B to A
What direction is the dr vector? Is it the direction of the line integral?

Say I want to derive the formula for electric potential due to a point in Space. E has a direction vector of ar
assume dL is pointing from infinity to A (-ar), which is opposite of the Eletric Field. And the formula ends up with a negative sign, which is not consistent with the formal formula.
Why?
 
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  • #2
The integral is you described, "Integral of ( E dot dL) from B to A", is $$\int_B^A \vec{E}\cdot\vec{dL}$$... that what you meant?

What direction is the dr vector? Is it the direction of the line integral?
dr points wherever you define it to point.

The integral is along a line, which, in general, will curve in most coordinate systems.
But does the potential difference in an electric field depend on the path taken? What does the rest of the theory say?

assume dL is pointing from infinity to A (-ar), which is opposite of the Electric Field. And the formula ends up with a negative sign, which is not consistent with the formal formula.
I think you may have misplaced a minus sign.
 
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What is voltage difference?

Voltage difference, also known as potential difference, is the difference in electric potential between two points in an electric circuit. It is measured in volts (V) and represents the amount of energy required to move a unit of electric charge from one point to another.

How is voltage difference calculated?

Voltage difference can be calculated using Ohm's Law, which states that voltage is equal to the product of current and resistance. It can also be calculated by measuring the difference in electric potential between two points using a voltmeter.

What is a line integral?

A line integral is a mathematical concept used to calculate the total change in a scalar or vector field along a specified curve or path. In the context of voltage difference, it is used to calculate the total change in electric potential along a given path in an electric circuit.

How is a line integral used to calculate voltage difference?

In an electric circuit, voltage difference can be calculated by integrating the electric field strength (measured in volts per meter) along a given path using a line integral. This involves multiplying the electric field strength at each point along the path by the distance traveled and summing up these values to get the total voltage difference.

Why is voltage difference important?

Voltage difference is important in understanding and analyzing electric circuits. It helps determine the flow of electric current and the amount of energy required for the circuit to function properly. It is also crucial in ensuring the safety of electrical appliances and preventing electrical hazards.

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