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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.

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.

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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