In each of the four cases belowa Gaussian circle is represented by the dashed line circle and the arrows represent electric field lines. In which of the four cases is the flux through the Gaussian circle not equal to zero? *** В
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- 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.Use GFSA (Given, Find, Solution, and Answer) on the given space below. Encircle your final answer, write it in scientific notation with 2 decimal places (if possible). Determine the electric flux for a Gaussian surface that contains 100 million electrons.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.
- Use GFSA (Given, Find, Solution, and Answer) on the given space below. Encircle your final answer, write it in scientific notation with 2 decimal places (if possible). An cylinder with radius 1 m and length 1.5 m has an infinite line of charge with a linear charge density of 30 C/m. (Make an illustration of the problem) (a) What is the total charge enclosed by the Gaussian cylinder? (b) What is the electric flux through the cylinder due to the infinite line of charge? (c) Calculate the electric field at a point 3 m away from the infinite line of charge.In the configuration shown in the picture below, what is the total pridicted electric field magnitude at point "a"A semicircle of radius a is in the first and second quadrants, with the center of curvature at the origin. Positive charge +Q is distributed uniformly around the left half of the semicircle, and negative charge −Q is distributed uniformly around the right half of the semicircle in the following figure. What is the magnitude and direction of the net electric field at the origin produced by this distribution of charge?
- 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).Discuss 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.A hollow sphere made from a non-conducting material is shown below in cross-section. The inner radius is R1, and the outer radius is R2. The material is charged uniformly -ρ.(a) Using Gauss’ Law, find an expression in terms R1, R2, and ρ of the magnitude(measured in N/C) and the direction (away from or towards the center) of the electricfield at a distance r from the center of the sphere, for values R1 < r < R2? (Do all thiswork symbolically - don't use the values of part (b) for this part.) (b) The inner radius is R1 = 1.00 cm, and the outer radius is R2 = 4.00 cm. Thematerial is charged uniformly ρ = -1.70 nC/m3. If the electric potential is 0V infinitely faraway, what is the electric potential at the outer surface (r = R2) of the sphere? Please show full work Thank you!
- Explain the electric flux of figure 12a using Gauss Law if there is another positive charge at r/2.A metal loop with a radius of 5 cm is in a B field of 15 T.What is the flux if the loop is parallel with the field?What is the flux if the angle is 30 degrees? What is the flux if the angle is 45 degrees? What is the flux if the angle is 60 degrees? What is the flux if the angle is 90 degrees?The figure below shows a section of a very thin, very long, straight rod with a uniform charge per unit length of λ. Point O is a perpendicular distance d from the rod. A spherical gaussian surface is centered at point O and has a radius R. (Use any variable or symbol stated above along with the following as necessary: ε0.) A)What is the electric flux through the spherical surface if R < d? B)What is the electric flux through the spherical surface if R > d?