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Review. A slab of insulating material (infinite in the y and z directions) has a thickness d and a uniform positive charge density ρ. An edge view of the slab is shown in Figure P23.45. (a) Show that the magnitude of the electric field a distance x from its center and inside the slab is E = ρx/ϵ0. (b) What If? Suppose an electron of charge −e and mass me can move freely within the slab. It is released from rest at a distance x from the center. Show that the electron exhibits
Figure P23.45
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Chapter 24 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- A solid insulating sphere of radius a = 5.00 cm carries a net positive charge of Q = 3.00 C uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius b = 10.0 cm and outer radius c = 15.0 cm as shown in Figure P24.54, having net charge q = 1.00 C Prepare a graph of the magnitude of the electric field due to this configuration versus r for O r 25.0 cm.arrow_forwardA solid plastic sphere of radius R1 = 8.00 cm is concentric with an aluminum spherical shell with inner radius R2 = 14.0 cm and outer radius R3 = 17.0 cm (Fig. P25.67). Electric field measurements are made at two points: At a radial distance of 34.0 cm from the center, the electric field has magnitude 1.70 103 N/C and is directed radially outward, and at a radial distance of 12.0 cm from the center, the electric field has magnitude 9.10 104 N/C and is directed radially inward. What are the net charges on a. the plastic sphere and b. the aluminum spherical shell? c. What are the charges on the inner and outer surfaces of the aluminum spherical shell? FIGURE P25.67arrow_forwardIn Figure P24.49, a charged particle of mass m = 4.00 g and charge q = 0.250 C is suspended in static equilibrium at the end of an insulating thread that hangs from a very long, charged, thin rod. The thread is 12.0 cm long and makes an angle of 35.0 with the vertical. Determine the linear charge density of the rod. FIGURE P24.49arrow_forward
- A slab of insulating material has a nonuniform positive charge density = Cx2, where x is measured from the center of the slab as shown in Figure P23.45 and C is a constant. The slab is infinite in the y and z directions. Derive expressions for the electric field in (a) the exterior regions (|x| d/2) and (b) the interior region of the slab (d/2 x d/2). Figure P23.45arrow_forwardA uniform electric field given by E=(2.655.35j)105N/C permeates a region of space in which a small negatively charged sphere of mass 1.30 g is suspended by a light cord (Fig. P24.53). The sphere is found to be in equilibrium when the string makes an angle = 23.0. a. What is the charge on the sphere? b. What is the magnitude of the tension in the cord? FIGURE P24.53arrow_forwardConsider the charge distribution shown in Figure P23.85. (a) Show that the magnitude of the electric field at the center of any face of the cube has a value of 2.18keq/s2. (b) What is the direction of the electric field at the center of the top face of the cube?arrow_forward
- A very long, thin wire fixed along the x axis has a linear charge density of 3.2 C/m. a. Determine the electric field at point P a distance of 0.50 m from the wire. b. If there is a test charge q0 = 12.0 C at point P, what is the magnitude of the net force on this charge? In which direction will the test charge accelerate?arrow_forwardThe infinite sheets in Figure P25.47 are both positively charged. The sheet on the left has a uniform surface charge density of 48.0 C/m2, and the one on the right has a uniform surface charge density of 24.0 C/m2. a. What are the magnitude and direction of the net electric field at points A, B, and C? b. What is the force exerted on an electron placed at points A, B, and C? FIGURE P25.47arrow_forwardA pyramid has a square base with an area of 4.00 m2 and a height of 3.5 m. Its walls are four isosceles triangles. The pyramid is in a uniform electric field of 655 N/C pointing downward (Fig. P25.13). What is the electric flux through the square base?arrow_forward
- Charge of uniform density ρ = 2.8 μC/m3 fills a nonconducting solid sphere of radius 5.1 cm. (a) What is the magnitude of the electric field 3.5 cm from the center of the sphere? __________N/C(b) What is it at 7.4 cm from the center of the sphere? ___________N/Carrow_forwardIn the figure, a thin glass rod forms a semicircle of radius r = 5.50 cm. Charge is uniformly distributed along the rod, with +q = 3.50 pC in the upper half and −q = −3.50 pC in the lower half. (a) What is the magnitude of the electric field at P, the center of the semicircle? _________N/C(b) What is its direction? ________° counterclockwise from the +x-axis (please include units in your solutions so that I can follow it easier)arrow_forwardAn infinite line of charge with linear density λ1 = 7.2 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.7 cm and outer radius b = 4.1 cm. The insulating shell is uniformly charged with a volume density of ρ = -556 μC/m3. a) What is λ2, the linear charge density of the insulating shell? b) What is Ey(P), the value of the y-component of the electric field at point P, located a distance 6.4 cm along the y-axis from the line of charge? c) What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.35 cm along a line that makes an angle of 30o with the x-axis?arrow_forward
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