Two large flat parallel sheets have opposite uniform surface charge densities ±o and are separated a distance d. A large, uncharged conducting slab of thickness d/3 is parallel to the charged sheets, centered between them. Find the electrostatic potential as a function of distance y perpendicular to the sheets. Take the reference potential V, = 0 and the origin y = 0 to be at the negative sheet. %3D
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- Problem 4: A small sphere with mass 1.5 g = 0.0015 kg hangs by a thread between two very large parallel vertical plates 5 cm = 0.05 m apart (see figure above on the right). The plates are insulating and have uniform surface charge densities +o and -o. The charge on the sphere is q = 8.9x 10-6 C. What potential WHAT IS THE CHARGE DENISTY ON EACH PLATE? IN nC/m^2 ! 30.0 -5.00 cmA uniform electric field is directed parallel to the +y-axis. If a positive test charge begins at the origin and moves upward along the y- axis, how does the electric potential vary, if at all? O The electric potential will increase with increasing y. O Too little information is given to answer this question. O The electric potential will decrease with increasing y. O The electric potential will remain constant with increasing y.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) =
- The drawling shows a plot of the electric potential V versus the displacement s. Determine the electric field in the region from 0.2 to 0.6 m. Be sure to include the proper + or - sign.8. Figure below shows a ring of outer radius R = 13.0 cm and inner radius l'inner = 0.200R. It has uniform surface charge density 0 = 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 = 2.00R from the center of the ring. 6 dQ K √ ₁7 - Pl What is your dQ? What is your infinitesimal area element? (a) Start with the formula for the potential: V = k What are your vectors r and r'? What is the distance to point P? What is dV? Potential due to a small ring of charge on the disk? (b) Write out the integral that you need to compute to get V. What are the bounds? (c) Once you get an expression for V, solve numerically. (d) Check to see if the units of your expression makes sense for V.A solid insulating sphere of radius a = 4 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly -118 µC/m³. Concentric with charged with a charge density p = the sphere is an uncharged spherical conducting shell of inner radius b = 12.8 cm, and outer radius c = 14.8 ст. P(40)
- Consider a thin, uniformly charged rod of length L with total charge Q and test points A, a distance a from the center of the rod and B a distance b from the rod. Find the potential difference between A and B first by integrating the point source potential to find VA and VB and subtracting, and then by integrating the field. Compare the results in the limit of L>>(a and b). To test the far field limit, compare the appropriate result to the case where L is much less than both a and b. You may need to do this one numerically.Problem 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). xQuestion BCalculate the surface electrical potential of each sphere before contact was made. Assume both spheres are initially very far away from each other, and let R = 0.5 m. Did the electric potential gradient inside the smaller sphere increase, decrease, or stay the same before compared to after contact was made? Why or why not? Calculate final surface electrical potential of each sphere after contact is made.A cylindrical shell of radius R, and height his charged with charge that is uniformly distributed over it surface. To find the electric potential due to this shell at point Pa distance d from its right base we take, as an element, a thin ring that has a charge element: ut of dx Select one: O dq = o(2 TRdx) O dq = o(2 Trdr) O dq = p(TR?dx) dq = o(TR?dx) Two concentric conducting spherical shells of radii a and bare charged to a total charge Q. If the two shells are connected as shown. Which of the following is false? en 5 ete D out of REDMI NOTE 9 144 AI QUAD CAMERASEE MORE QUESTIONS