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Electric Field of Uniformly Charged Rod at bisector Pythagoras i e r 2 = d 2 + (l 2) 2 The Attempt at a Solution Starting out with replacing the infinitesimal d q in integral with λ d l to give an expression of E → = k e λ ∫ d l r 2 r ^ (I took the λ outside the integral since it is uniform and thus I assumed it was a constant) From there I could only find one way to continue
Electric Field of a Uniform Ring of Charge • Physics Forums Some suggest that the integral of charge elements across the ring sums to the total charge, while others discuss the implications of using definite integrals versus indefinite integrals in physics problems The discussion is ongoing, with various perspectives on the use of integration limits and constants being shared
Ideal Gas Equation and Polytropic Constant • Physics Forums The original poster attempts to derive the work done using the integral of pressure and volume, while questioning the validity of substituting different forms of the ideal gas equation Participants raise concerns about the interpretation of the variable "n" in different contexts and the implications for volume calculations
Why integrating sin^2(wt) gives the half-period? - Physics Forums In an exercise with included solution I can't understand how integrating sin^2(ωt) gives T(period) 2 \\intsin^2(ωt)dt = Period 2 I posted the whole problem below, because I had more doubts, but understood them typing up the problem I appreciate any help [SIZE="2"]YOU CAN
Electric Field Produced by a Finite Charged Wire - Physics Forums The problem involves calculating the electric field produced by a finite charged wire with a linear charge density at a specific point above its midpoint The context is rooted in electrostatics and requires the application of integral calculus to derive the electric field expression in terms of given parameters Exploratory, Mathematical reasoning, Problem interpretation Participants discuss
Understanding Integration of 1 (x^2 + a^2) and the Role of the Tan . . . There is a suggestion to evaluate the indefinite integral ∫ (1 (1+x²))dx as a starting point for understanding the integration of 1 (x² + a²) Participants discuss using the substitution x = tan (y) to compute the integral, indicating that this method is effective for transforming the integral into a more manageable form
Can the Volume of a Sphere be Calculated by Integrating the Area of . . . The the area integral is a double integral over r and the azimuthal angle The volume integral is over r, the azimuthal angle and the polar angle You're missing some parts of the "big picture" about spherical coordinates You kind of skipped the intergrating over the azimuthal angle part by including straight into your integrand
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