A conducting sphere of radius 'a' has a constant electric potential at its surface equal to V(a,0) = kcos(20) where k is a constant and 0 is the usual spherical coordinate. Calculate the electric potential in the enclosed region consisting of everywhere outside of this conducting sphere. HINT: use the double angle identity cos(2x) = 2 cos²(x) — 1.
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- A charged conducting spherical shell of radius R = 3 m with total charge q = 23 μC produces the electric field given by E⃗ (r)={014πϵ0qr2r̂ forforr<Rr>R(PICTURE ATTACHED OF EQUATION) a. Enter an expression for the electric potential inside the sphere ( r < R ) in terms of the given quantities, assuming the potential is zero at infinity. V(r)= b. Calculate the electric potential, in volts, at radius r inside the charged shell. V(r) =For a spherical surface with radius 0.15 m and is charged by 29 nC, the electric Potential V at r = 0.39 m is (in V) Select one:a. 1740b. 1716c. 669d. 0e. 11600E1.3
- The charge density on a disk of radius R = 11.2 cm is given by σ = ar, with a = 1.34 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 48.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. V R AProblem 2: A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder? a) Compute the surface charge density n of the shell from its total charge and geometrical parameters. Vcenter = 1 Q 2 In 4л€ L t₂ S² b) Which charge dq is enclosed in a thin ring of width dz located at a distance z from the center of the cylinder (shown in Fig.2)? Which potential dV does this ring create at the center (you need to use the formula derived in the textbook for the potential of a charged ring along its axis). dz c) Sum up the contributions from all the rings along the cylinder by integrating dV with respect to z. Show that (The integral that you need to use here is d dt √²+a² R² + 1/2 + 1/1/20 √√R² +4-4 L² R2 L R FIG. 2: The scheme for Problem 2 [2 = ln(t + √₁² + a²) 1².) 2A ring of charge of radius a lies in the z = 0 plane and centered on the z-axis. The charge density on the ring is given by p(') = Peo cosp' [C/m]. First, find the electric field at any point on the z-axis, Ē(z). Next, find the potential Þ(z) on the z-axis. Explain why the field in this problem cannot be found by taking the gradient of your answer for Þ(z). xCurrent Attempt in Progress - Your answer is partially correct. The figure shows a ring of outer radius R = 25.0 cm, inner radius r = 0.290R, and uniform surface charge density 0 = 2.10 pC/m². With V = 0 at infinity, find the electric potential at point P on the central axis of the ring, at distance z = 1.10R from the center of the ring. Number i 1.186E-3 Units V OThe charge density on a disk of radius R = 11.6 cm is given by o = ar, with a = 1.46 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 44.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. V R AWhat is the potential difference V(r) – V(0) for r < a (i.e., where r is inside the insulating sphere, and V(0) is the potential at the origin)?Please answer parts (a) and (b), showing all work.Please asap4. Figure below shows a ring of outer radius R = 13.0 cm, inner radius r= 0.200R, and uniform surface charge density o = 6.20 pC/m2. With V = 0 at infinity, find the electric potential at point P on the central axis of the ring, at distance z = 2.0OR from the center of the ring. %3D RSEE MORE QUESTIONS