What is line integral of electric field ? What does it indicate ?
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The multiplication of electric field and the path length gives Line integral of electric Field.
Let there be two point A and B on a non uniform electric field (magnitude and direction at every point is different). The irregular line denotes the path travelled by charge. With changing Electric field, the path travelled by a charge also changes at every point on the curve.
To find line integral at every point, take a very small length dl on the path. So that dl makes a certain angle θ with the electric field. On resolving dl into two components as dlcosθ and dlsinθ the component
of dl along E is dl cosθ. As shown in figure.
Potential difference dV = Edr.
So line integral to move charge from A to B = A∫B EdrCosθ
VA - VB = A∫B E→.dr→
To move charge from B to A (VA - VB) = - B∫A E→.dr→
Note-
In a variable electric field, potential difference between two point is equal to negative of line integral of electric field.
#BeBrainly
Let there be two point A and B on a non uniform electric field (magnitude and direction at every point is different). The irregular line denotes the path travelled by charge. With changing Electric field, the path travelled by a charge also changes at every point on the curve.
To find line integral at every point, take a very small length dl on the path. So that dl makes a certain angle θ with the electric field. On resolving dl into two components as dlcosθ and dlsinθ the component
of dl along E is dl cosθ. As shown in figure.
Potential difference dV = Edr.
So line integral to move charge from A to B = A∫B EdrCosθ
VA - VB = A∫B E→.dr→
To move charge from B to A (VA - VB) = - B∫A E→.dr→
Note-
In a variable electric field, potential difference between two point is equal to negative of line integral of electric field.
#BeBrainly
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