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Question

Consider an electric field \(\vec{E}\) and two points in space, \(a\) and \(b\), the work required to move a test charge \(Q\) from \(a\) to \(b\) is [...]

Answer
\(W=\int^{b}_{a}\vec{F}\cdot d\vec{l}=-Q\int^{b}_{a}\vec{E}\cdot d\vec{l}\) and becasue of the electrostatic field and the stokes's theorem, we have \(\oint_{P}\vec{E}\cdot d\vec{l}=\int_{S}(\nabla\times\vec{E})\cdot d\vec{a}=0\) for any closed path.

Question

Consider an electric field \(\vec{E}\) and two points in space, \(a\) and \(b\), the work required to move a test charge \(Q\) from \(a\) to \(b\) is [...]

Answer
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Question

Consider an electric field \(\vec{E}\) and two points in space, \(a\) and \(b\), the work required to move a test charge \(Q\) from \(a\) to \(b\) is [...]

Answer
\(W=\int^{b}_{a}\vec{F}\cdot d\vec{l}=-Q\int^{b}_{a}\vec{E}\cdot d\vec{l}\) and becasue of the electrostatic field and the stokes's theorem, we have \(\oint_{P}\vec{E}\cdot d\vec{l}=\int_{S}(\nabla\times\vec{E})\cdot d\vec{a}=0\) for any closed path.
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The work it takes to move a charge in static E field
Consider an electric field \(\vec{E}\) and two points in space, \(a\) and \(b\), the work required to move a test charge \(Q\) from \(a\) to \(b\) is \(W=\int^{b}_{a}\vec{F}\cdot d\vec{l}=-Q\int^{b}_{a}\vec{E}\cdot d\vec{l}\) and becasue of the electrostatic field and the stokes's theorem, we have \(\oint_{P}\vec{E}\cdot d\vec{l}=\int_{S}(\nabla\times\vec{E})\cdot d\vec{a}=0\) for any closed path.

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