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Figure 23-29 shows four Gaussian surfaces consisting of identical cylindrical midsections but different end caps. The surfaces are in a uniform electric field
Figure 23-29 Question 12.
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Fundamentals of Physics, Volume 1, Chapter 1-20
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- Figure P23.23 represents the top view of a cubic gaussian surface in a uniform electric field E oriented parallel to the top and bottom faces of the cube. The field makes an angle with side , and the area of each face is A. In symbolic form, find the electric flux through (a) face , (b) face , (c) face , (d) face , and (e) the top and bottom faces of the cube. (f) What is the net electric flux through the cube? (g) How much charge is enclosed within the gaussian surface? Figure P23.23arrow_forwardTwo infinite, nonconducting sheets of charge are parallel to each other as shown in Figure P19.73. The sheet on the left has a uniform surface charge density , and the one on the right hits a uniform charge density . Calculate the electric field at points (a) to the left of, (b) in between, and (c) to the right of the two sheets. (d) What If? Find the electric fields in all three regions if both sheets have positive uniform surface charge densities of value .arrow_forwardThe figure shows two concentric insulating thin spherical shells: Sphere 1 of radius R₁ = R cm and a total charge Q₁ = +Q nC. Sphere 2 of radius R₂ = 2R cm and a total charge Q2 = -40 nC. Take R-25 cm and Q-90 nC E = +Q R E= B 1. Find the magnitude of the net electric field at a distance r= 91 cm from the center of the two spheres. [N/C] E = 2. The net electric filed vector at a distance r= 91 cm from the center of the two spheres is pointing: Ooutward 40 3. Find the magnitude of the net electric field at a distance r= 41 cm from the center of the two spheres. [N/C] 2R Oinward 4. Find the magnitude of the net electric field at a distance r= 21 cm from the Ct...er of the two spheres. + [N/C] 5. What is the direction of the electric field E₂ created by Ring 2 at point P Direction: 6. Write the expression of the electric filed E₂ created by Ring 2 at point P. Ē₂ = > [N/C] 7. If vector E₁ = [N/C] and vector E₂ = [N/C]. Find the net electric filed Enet at point P. Enet = [N/C] > [N/C] 8. If…arrow_forward
- d L In Fig-1, there is a rod of length LA = 49 cm is lying on the x -axis whose one end is placed at the origin. It carries a uniform linear charge density AA = -21 µC/cm. The point P is located on the x-axis at a distance d = 10 cm from the origin as shown in the figure. a) Find the electric field in unit vector notation at point P due to the rod A. I component of the electric field Give your answer to at least three significance digits. N/C y component of the electric field Give your answer to at least three significance digits. N/Carrow_forwardA uniformly charged ring of charge +Q and radius R lies in the x-y plane, and at some point along the axis of the ring a distance z from the center you measu re the magnitude of the electric field E. Replacing the ring with a solid disk having the same Q and R, you would measure D a. Edisk Eringarrow_forwardTwo identical large conducting plates carry equal and opposite charges, has created a uniform electric field of 2. 8 kN/C as shown in Figure. The separation between the plates is 1 = 6.50 mm. What is surface charge density o the plates? + + + +arrow_forward
- A semicircle of radius a is in the first and second quadrants, with the center of curvature at point P. Positive charge +Q is distributed uniformly around the left half of the semicircle, and negative charge is distributed uniformly around the right half of the semicircle. What is the net electric field at the origin produced by this charge distribution? (modified from Young & Freedman, 2011, Problem 21-98) +Q Parrow_forward+Q dQ Consider a thin plastic rod bent into a semicircular arc of radius R. with center at the origin as shown in the figure. The rod carries a unformly distributed positive charge +Q. Let a point on the arc be specified by an angle 0, where 0 is measured from the positive y axis and increases in the counter-clockwise direction. Throughout this problem, use for Coulomb's constant. Determine the electric field dat the origin due to the indicated infinitesimal piece of the rod at an angle 0, that subtends an angle A0. Express your answer in terms of 0, A0, R. Q and fundamental constants. dB₂ (Q*k*Deltatheta)/(R^2 *theta) X Q.k. AO R².0 dEy= de 0 (Q*k*Deltatheta)/(cos(theta) X Q.k. A0 cos (0) R² dE, - 0arrow_forwardA 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->.arrow_forward
- to s In the figure a solid sphere of radius a= 3.40 cm is concentric with a spherical conducting shell of inner radius b-2.00a and outer radius c2.40a. The sphere has a net uniform charge q +2.77 fC; the shell has a net charge q2= -91. What is the magnitude of the electric field at radial distances (a) r0 cm, (b) r a/2.00. (c) r=a, (d) r- 1.50a, (e) r=2.30a, and (f)r=3.50a? What is the net charge on the (g) inner and (h) outer surface of the shell? doc (a) Number Units (b) Number Units se (c) Number Units ase (d) Numbe Units mlarrow_forwardAn insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is p = 3B / r3/2 (division) where is a constant and r is the distance from the center of the sphere. What is electric field at any point inside the sphere?Continuation of the problem can be seen in the images. Thanks!arrow_forwardThe figure shows two parallel nonconducting rings with their central axes along a common line. Ring 1 has uniform charge 9₁ and radius R; ring 2 has uniform charge 92 and the same radius R. The rings are separated by a distance 3.00R. The ratio of the electric field magnitudes of Ring 1 and Ring 2 at point P on the common line is 3.46. What is the ratio of charge magnitudes 91/92? nber i Ring 1 91 O Ring 2 R 92 Units No unitsarrow_forward
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