FIG I A thin ring of radius R lies in the ry plane, centred ou the...

   

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FIG I A thin ring of radius R lies in the ry plane, centred ou the -axis. The ring has four uncharged insulating pieces (dark patches of Fig 1) and four metallic arcs. Two of these metallic ares have charge q and two have charge q2, syinmetrically placed about (r.y. =) = (0,0.0) as shown in Fig. 1. (a) Write the small element of the electric potential dV at height z along the -axis due to a small element of charge day as shown on Fig. 1. (Hint: assume this small element of charge it is Small enough to treat as a poimt charge.) 12 R. V(2) 2282 (b) Write the small element of the electric potential dV2 at height z along the z-axis due to a small element of charge dq2 as shown on Fig. 1. /2 (c) For any small element of charge dq on either patch of charge q1, would you get the result found in (a)? Explain why or why not. (Assume that you are breaking up one of the patches of total charge qi into equal sized elements of charge dg). /2 (d) Integrate your expressions from parts (a) and (b) to find the total electric potential due to this ring along the z-axis at z = 3 m. 13 (e) Assuming that the charged patches are of equal sizes and on opposite sides of the ring, as shown in Fig. 1, explain what direction the electric field of this ring would have to point in and why. /4 /4 (f) Find the s-component of the electric field due to this ring at height 2. (f) Find the z-component of the electric field due to this ring at height z. 14 (g) If q = 2µuC and q2 = -1µC, R = 4m and z = u = 10-6 and K = 9.0 ×10°N m). 3m, find V and E (Note: %3D %3D 13 FIG I A thin ring of radius R lies in the ry plane, centred ou the -axis. The ring has four uncharged insulating pieces (dark patches of Fig 1) and four metallic arcs. Two of these metallic ares have charge q and two have charge q2, syinmetrically placed about (r.y. =) = (0,0.0) as shown in Fig. 1. (a) Write the small element of the electric potential dV at height z along the -axis due to a small element of charge day as shown on Fig. 1. (Hint: assume this small element of charge it is Small enough to treat as a poimt charge.) 12 R. V(2) 2282 (b) Write the small element of the electric potential dV2 at height z along the z-axis due to a small element of charge dq2 as shown on Fig. 1. /2 (c) For any small element of charge dq on either patch of charge q1, would you get the result found in (a)? Explain why or why not. (Assume that you are breaking up one of the patches of total charge qi into equal sized elements of charge dg). /2 (d) Integrate your expressions from parts (a) and (b) to find the total electric potential due to this ring along the z-axis at z = 3 m. 13 (e) Assuming that the charged patches are of equal sizes and on opposite sides of the ring, as shown in Fig. 1, explain what direction the electric field of this ring would have to point in and why. /4 /4 (f) Find the s-component of the electric field due to this ring at height 2. (f) Find the z-component of the electric field due to this ring at height z. 14 (g) If q = 2µuC and q2 = -1µC, R = 4m and z = u = 10-6 and K = 9.0 ×10°N m). 3m, find V and E (Note: %3D %3D 13 FIG I A thin ring of radius R lies in the ry plane, centred ou the -axis. The ring has four uncharged insulating pieces (dark patches of Fig 1) and four metallic arcs. Two of these metallic ares have charge q and two have charge q2, syinmetrically placed about (r.y. =) = (0,0.0) as shown in Fig. 1. (a) Write the small element of the electric potential dV at height z along the -axis due to a small element of charge day as shown on Fig. 1. (Hint: assume this small element of charge it is Small enough to treat as a poimt charge.) 12 R. V(2) 2282 (b) Write the small element of the electric potential dV2 at height z along the z-axis due to a small element of charge dq2 as shown on Fig. 1. /2 (c) For any small element of charge dq on either patch of charge q1, would you get the result found in (a)? Explain why or why not. (Assume that you are breaking up one of the patches of total charge qi into equal sized elements of charge dg). /2 (d) Integrate your expressions from parts (a) and (b) to find the total electric potential due to this ring along the z-axis at z = 3 m. 13 (e) Assuming that the charged patches are of equal sizes and on opposite sides of the ring, as shown in Fig. 1, explain what direction the electric field of this ring would have to point in and why. /4 /4 (f) Find the s-component of the electric field due to this ring at height 2. (f) Find the z-component of the electric field due to this ring at height z. 14 (g) If q = 2µuC and q2 = -1µC, R = 4m and z = u = 10-6 and K = 9.0 ×10°N m). 3m, find V and E (Note: %3D %3D 13 FIG I A thin ring of radius R lies in the ry plane, centred ou the -axis. The ring has four uncharged insulating pieces (dark patches of Fig 1) and four metallic arcs. Two of these metallic ares have charge q and two have charge q2, syinmetrically placed about (r.y. =) = (0,0.0) as shown in Fig. 1. (a) Write the small element of the electric potential dV at height z along the -axis due to a small element of charge day as shown on Fig. 1. (Hint: assume this small element of charge it is Small enough to treat as a poimt charge.) 12 R. V(2) 2282 (b) Write the small element of the electric potential dV2 at height z along the z-axis due to a small element of charge dq2 as shown on Fig. 1. /2 (c) For any small element of charge dq on either patch of charge q1, would you get the result found in (a)? Explain why or why not. (Assume that you are breaking up one of the patches of total charge qi into equal sized elements of charge dg). /2 (d) Integrate your expressions from parts (a) and (b) to find the total electric potential due to this ring along the z-axis at z = 3 m. 13 (e) Assuming that the charged patches are of equal sizes and on opposite sides of the ring, as shown in Fig. 1, explain what direction the electric field of this ring would have to point in and why. /4 /4 (f) Find the s-component of the electric field due to this ring at height 2. (f) Find the z-component of the electric field due to this ring at height z. 14 (g) If q = 2µuC and q2 = -1µC, R = 4m and z = u = 10-6 and K = 9.0 ×10°N m). 3m, find V and E (Note: %3D %3D 13