Taking Ap physics C this coming year

[mapletree7]

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@WiseGuy

I think you may be confusing trig substitution with basic (“u”) substitution. When you integrate an e-field or potential over a loop/line/disc/etc., you aren’t doing trig sub. Trig sub is also not part of the Calc BC curriculum. You’d need to do trig substitution when you have something like integral dx / sqrt(a^2-x^2). Your substitution then is x=a*sinθ.

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<p>Are you sure it’s not part of the Calculus BC curriculum? I’m 100% sure it was covered in the course I took. Maybe it’s not on the exam - although I find that a bit ridiculous, as trigonometric substitution is a key part of any single-variable calculus course.</p>

<p>In any case, you need it in order to calculate potentials or fields of continuous charge distributions. Consider a line of charge, and a point a distance h above the left end. Suppose we want to calculate the potential due to the charge distribution at this point. For an arbitrary element dq a distance x from the left end, the distance from the element to the point is r = sqrt( h^2 +x^2). As dV = 1/4\pi \epsilon_0 dq/r and dq = lambda dx, we have an integral of the form 1/sqrt(a^2 + x^2), which requires trig substitution (x = a tan u), or hyperbolic substitution.</p>

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@WiseGuy

Partial derivatives also don’t come up in the AP Physics C: E&M Course. Depending on your class, you may see them hinted at when talking about the differential relationship between e-field and potential, where E = -grad(V). The gradient operator there tells you to use partial derivatives when dealing with a multidimensional potential, but all you need for the AP exam is simply E = -dV/dx.

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<p>You’re right there, and I should have acknowledged this in my post. The course I took explicitly covered partial derivatives in the context of the relation between potential and E, but it would vary.</p>