Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Compute for the work done, in millijoules, in moving a 8-nC charge radially away from the center from a distance of 7 m to a distance of 11 m against the electric field inside a non-conducting spherical shell of inner radius 3 m, outer radius 17 m, and total charge 8 mC.
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- Repeat the preceding problem, with E=2xi+3x2k.arrow_forwardExamine the summary on page 780. Why are conductors and charged sources with linear symmetry, spherical symmetry, and planar symmetry categorized as special cases rather than major concepts or underlying principles?arrow_forwardFind all the bound charges and the total charge of a dielectric sphere of radius a carrying polarization P = rr ̂ ?arrow_forward
- Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. Imagine a small metal ball of mass m and negative charge −q0. The ball is released from rest at the point (0,0,d) and constrained to move along the z axis, with no damping. If 0<d≪a, what will be the ball's subsequent trajectory? repelled from the origin attracted toward the origin and coming to rest oscillating along the z axis between z=d and z=−d circling around the z axis at z=darrow_forwardHello, I understand that to calculate the net charge in the shell, I need to integrate the equation from 4 cm to 6 cm with volume charge density times 2 * pi * r * dr. However, since the problem here provides me with a novel expression of p = b/r, I am a bit lost... Could you please tell me how I can solve such problem?arrow_forwardRe-derive Gauss’s law for the gravitational field, with g → directed positively outward.arrow_forward
- A large non-conducting slab of area A and thickness d has a charge density rho=Cx^4. The origin is through the center of the slab. That is to say, it bisects the slab into two equal volumes of d/2 thickness and with an area of A, with -d/2 to the left of x=0, and d/2 to the right of x=0. Express all answers in terms of C, x, and any known constants. Gaussian surface 1 (cylinder) is located such that its volume encompasses the charge contained within the slab. Apply Gauss's Law to cylinder 1 to determine the electric field to the left and to the right of the slab. Make sure you incude the domains over which the field is valid.arrow_forwardReformulate Gauss’s law by choosing the unit normal of the Gaussian surface to be the one directed inward.arrow_forwardA point particle moves in space under the influence of a force derivablefrom a generalized potential of the formU(r, v) = V (r) + σ · L,where r is the radius vector from a fixed point, L is the angular momentumabout that point, and σ is the fixed vector in space. Find the components of the force on the particle in spherical polar coordinates, on the basis of the equation for the components of the generalized force Qj: Qj = −∂U/∂qj + d/dt (∂U/∂q˙j)arrow_forward
- What is the electrostatic force on the particle at the lower-right-hand corner of the square shown here? Write the result in terms of the quantities given in the problem (q, a, and k (Coulomb’s constant). Don’t forget to include both the magnitude and the direction of the net force on that charge.arrow_forwardConsider an infinitesimal segment located at an angular position θ on the semicircle, measured from the lower right corner of the semicircle at x=a, y=0. (Thus θ=π2 at x=0, y=a and θ=π at x=−a, y=0.) What are the x- and y- components of the electric field at point P (dEx and dEy) produced by just this segment? Express your answers separated by a comma in terms of some, all, or none of the variables Q, a, θ, dθ, and the constants k and π.arrow_forwardA block having mass m and charge +Q is connected to an insulating spring having a force constant k. The block lies on a frictionless, insulating, horizontal track, and the system is immersed in a uniform electric field of magnitude E directed as shown. The block is released from rest when the spring is unstretched (at x = 0). We wish to show that the ensuing motion of the block is simple harmonic. (a) Consider the system of the block, the spring, and the electric field. Is this system isolated or nonisolated? (b) What kinds of potential energy exist within this system? (c) Call the initial configuration of the system that existing just as the block is released from rest. The final configuration is when the block momentarily comes to rest again. What is the value of x when the block comes to rest momentarily? (d) At some value of x we will call x = x0, the block has zero net force on it. What analysis model describes the particle in this situation? (e) What is the value of x0? (f)…arrow_forward
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