Use Gauss's law (OE•dà ) to show that the electric field a distance r away from the axis enc of an infinitely long straight wire with a uniform charge per length 2 (shown below) is given by Ē = 2arɛ, show your steps and include a clear diagram showing the vectors E and dA.
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- Consider a very thin semi-circle of charge as shown, with radius of R. Explain with words and equations how you would derive the electric field vector measured at the center of this line of charge curved into a semi-circle with radius R (Measure E at the origin).Consider an electric field map, and in one region of the map the electric field lines are closer together than in other regions of the map. What does this imply? Give your answer in 2-3 well written sentences.Consider a quarter-circular, very thin, curved rod with a uniform linear charge density, λ, and aradius, r. Derive an equation for the magnitude of the electric field at the point, P, at the centercurvature of the rod, as shown in the figure below. Write the final answer in terms of λ and r, and simplify your answer as much as possible.
- In the configuration shown in the picture below, what is the total predicted angle for electric field at point a?Find the electric field a distance z above the center of a flat circular disk of radius R (See attatched figure) that carries a uniform surface charge σ. What does your formula give in the limit R → ∞? Also check the case z >> R.The figure shows a uniformly charged rod withlength a, carrying a total charge of Q. You needto derive an expression for the electric field gen-erated by the rod at point P, which is a distanced below the left end of the rod. (a) Redraw the figure and show clearly how you planto parametrise the rod. Indicate a general in-finitesimal segment and include any vectors rele-vant to your calculation. This figure is an inte-gral part of your calculation, and should providethe reader with enough information to be able tofollow your work. (b) Write down an expression for dE~ , the electric fieldgenerated at point P by an infinitesimal segment.Ensure that the dependence on the parametrisa-tion coordinate is explicit in your expression. (C) Write down an expression for dEx, the x-component of dE~ , and calculate Ex, the x-component of the field at point P. (d) Repeat the steps above to determine the y-component of the field at point P.
- Calculate the electric flux traversing a rectangle with a surface area of 67 m², a uniform electric field of 122 N/C, and angle of 34° from the horizontal. Show the given and the complete and detailed solutionThree equal charges are located at the vertices of a right isosceles triangle as shown below. What is the magnitude and direction of the resultant electric field at the midpoint M of BC?A non-uniform thin rod is bent into an arc of radius R. The linear charge density λ of the roddepends on θ and is given byλ =λ0/cos θwhere λ0 is a positive constant. The arc extends from θ =π/4 to θ =3π/4as shown a)Sketch the direction of the resultant electric field at the origin.b) Calculate the magnitude of the electric field E->.
- Find the electric field of an infinite, flat sheet with charge distribution σ = 17.7 ×10^−12C/m2 by integrating the field produced and by using Gauss’s law. Now thatyou found the electric field of this sheet, we produce a hole of radius 15 m on thesheet and we ask you to find the electric field of this new sheet 52.7 m away fromthe infinite sheet on the central axis of the hole. Mind helping me out please, I got a few steps in but not sure where to go so I'm convinced I'm doing it wrong. I asked some peers and they said the answer was 0.96. ThanksA line of uniform charge Q runs along the y-axis from 0 to L. What is the electric field at the position (x0, 0)? Solve by creating an integral and simplifying itDiscuss the possibility of choosing Gaussian surface other than the sphere.For instance what if you choose the cylindrical surface as a Gaussian surface, is it possible to use Gauss’s law in order to calculate the electric fieldof a charged sphere? Explain your answer in detail.