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This quiz contains 8 practice questions covering Electrodynamics 2.

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Electrodynamics 2 Practice Quiz

Test your knowledge of Electrodynamics 2 with 8 practice questions. Get instant feedback and detailed explanations to identify gaps and improve your understanding.

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Question 1 of 80 answered

Under a boost in the

x

-direction with velocity parameter

\beta=v/c

, the four-position transforms as

x'^0=\gamma(x^0-\beta x^1)

x'^1=\gamma(x^1-\beta x^0)

. The four-gradient transforms as

\partial'_0=\gamma(\partial_0+\beta\partial_1)

\partial'_1=\gamma(\partial_1+\beta\partial_0)

. Why do the gradient components have the opposite sign in the

\beta

terms compared to the position components?

Incorrect

Correct answer: Because the gradient is a covariant object and lower indices transform with the inverse Lorentz matrix, ensuring scalar products remain invariant.

The gradient $\partial_\mu$ has a lower index (is covariant) and thus transforms with the inverse Lorentz matrix. This gives the opposite sign in the $\beta$ terms relative to the contravariant four-position $x^\mu$. The opposite transformation guarantees invariance of scalar products like $\partial_\mu x^\mu$. (Source: practical_advice_detailed (1).pdf)

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