- #1
ewr
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- 0
In the problem attached, why is the integral become just the length of line cf?
Last edited:
Calculating Length of Line cf: A Math Problem Explained
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The discussion centers on understanding why the integral in the math problem simplifies to the length of line cf. This simplification is derived from the definition of a line integral, specifically when evaluating the work done by an electric field along a straight path. The integral is expressed as the product of the electric field strength and the distance, leading to the formula V_f - V_i = -Ed. The key takeaway is that the integral reduces to the length of the line when the path is straight and the angle is zero. This explanation highlights the relationship between electric fields and line integrals in physics.
In the problem attached, why is the integral become just the length of line cf?
- #2
Nugatory
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ewr said:
That result pretty much follows from the definition of a line integral. If you're not familiar with that concept, google will find you some pretty decent explanations.
- #3
jtbell
Staff Emeritus
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Note that in part (a) the integral becomes just the length of line if, that is, d.
$$V_f - V_i = -\int^f_i {\vec E \cdot d\vec s}
= -\int^f_i {E(\cos 0^\circ)ds} = -E \int^f_i {ds} = -Ed$$
$$V_f - V_i = -\int^f_i {\vec E \cdot d\vec s}
= -\int^f_i {E(\cos 0^\circ)ds} = -E \int^f_i {ds} = -Ed$$
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