the electric field due to a uniformly charged ring of radius R and total charge Q>0 above its center. A small test charge q < 0 is released from z = 00 with zero initial speed. (b) The moment the test charge passes the center point, the radius of the circular ring is halved and its charge is doubled. What is the maximum distance that the test charge can move along the z-axis?
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- The electric field in an xy plane produced by a positively charged particle is 8.29(5.9 i + 5.3 Ĵĵ) N/C at the point (4.2, 4.0) cm and 100 î N/C at the point (4.6, 0) cm. What are the (a) x and (b) y coordinates of the particle? (c) What is the charge of the particle? (a) Number i Units (b) Number i Units (c) Number i UnitsA uniformly charged rod of length L = 1.2 m lies along the x-axis with its right end at the origin. The rod has a total charge of Q = 6.8 μC. A point P is located on the x-axis a distance a = 2.4 m to the right of the origin.Write an equation for the electric field dE at point P due to the thin slide of the rod dx. Give your answers in terms of the variables Q, L, x, a, dx, and the Coulomb constant, k. Notice that the coordinate x will be less than zero over the length of the rod.A helium nucleus (mass = 6.64×10−27kg, net charge = +2e)is fired directly toward a spherical conductor on a radially inward path. The conductor, which is fixed in place, has radiusR= 0.55 m and surface charge densityσ= +12 nC/m2. If the helium nucleus is initially very far away from the conductor, then what initial speed must it be given so that it just barely avoids touching the surface of the conductor before being repelled back to infinity? Make sure to draw a voltage vs. position curve for the spherical conductor as part of your representation.
- +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, where is measured from the positive y axis and increases in the counter- clockwise direction. Throughout this problem, usek for Coulomb's constant. k-Q Rª Determine the electric field at the origin due to the indicated infinitesimal piece of the rod at an angle, that subtends an angle A. Express your answer in terms of , AP, R, Q and fundamental constants dE, - (*1/2 dE deA charge of 20 nC is uniformly distributed along a straight rod of length 4.0 m that is bent into a circular arc with a radius of 2.0 m. What is the magnitude of the electric field at the center of curvature of the arc?In the figure an electron (e) is to be released from rest on the central axis of a uniformlý charged disk of radius R. The surface charge density on the disk is + 4.27 µC/m2. What is the magnitude of the electron's initial acceleration if it is released at a distance (a) R, (b) R/ 139, and (c) R/ 1270 from the center of the disk? (a) Number Units Units (b) Number Units (c) Number
- A sphere of uniform charge density rho=10^−6 C/m 3 has a small hole drilled along its diameter, forming a tunnel from one end of the sphere to the other. An electron is released at the opening of the tunnel and begins to move, speeding up towards the center of sphere. After it passes the center of the sphere, it begins to slow down until it reaches the other end of the tunnel and stops. The electron then moves back up to the first opening and start the cycle again. It repeats this cycle many times. Find the frequency of this cyclic motion.Four concentric very long cylindrical shells (made of thin plastic) of radii a, b, c and d have charges +Q, -Q, +Q and -Q per one meter of length of cylinders, respectively. The cross-section of the cylindrical shells is shown in the figure below. Assume that charges are uniformly distributed. Determine the magnitude of the electric field at points A, B, C and D, which are at radial distances Ra, Rg, Rc and Rp, from the center of the smallest cylindrical shell. Express the answers in terms of Q, RA, R3, Rc, Rp and constants. A·B •C •D dProblem 12: A uniformly charged rod of length L = 1.4 m lies along the x-axis with its right end at the origin. The rod has a total charge of Q = 8.2 μC. A point P is located on the x-axis a distance a = 1.8 m to the right of the origin. Part (a) Consider a thin slice of the rod of thickness dx located a distance x away from the origin. What is the direction of the electric field at point P due to the charge on this thin slice of the rod? Part (b) Write an equation for the electric field dE at point P due to the thin slide of the rod dx. Give your answers in terms of the variables Q, L, x, a, dx, and the Coulomb constant, k. Notice that the coordinate x will be less than zero over the length of the rod. Part (c) Integrate the electric field contributions from each slice over the length of the rod to write an equation for the net electric field E at point P. Part (d) Calculate the magnitude of the electric field E in kilonewtons per coulomb (kN/C) at point P due to the charged…
- What is the percent difference between the electric field produced by the finite disk and by an infinite sheet with the same charge per unit area at x = 0.40 cm?Chapter 23, Problem 038 In part (a) of the figure an electron is shot directly away from a uniformly charged plastic sheet, at speed vs-2.80 x 105 m/s. The sheet is nonconducting, flat, and very large. Part (b) of the figure gives the electron's vertical velocity component v versus time t until the return to the launch point. What is the sheet's surface charge density? 09 0 18.0 (ps) Number Units the tolerance is +/-2%can you please ans (k) & ( l)?