7. Consider the following contour C made of two semi-circles:yLox(2d,0)(-2d,0)Evaluate the contour integralE ds,if E is a constant electric field given by (a) E =and (b) E = (0, E). (Hint: Make use of the fact that theelectric field is a conservative field.)

Answered: Image /qna-images/answer/4ec87c77-5ee3-47f7-b9ef-35bcc9fd45f5.jpg

Answered: 7. Consider the following contour C…

University Physics Volume 2

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Chapter6: Gauss's Law

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Problem 63P: A long cylinder of copper of radius 3 cm is charged so that it has a uniform charge per unit length...

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A thin, square, conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 108 C is placed on the plate. Find (a) the charge density on each face of the plate, (b) the electric field just above the plate, and (c) the electric field just below the plate. You may assume the charge density is uniform.
An infinitely long line charge having a uniform charge per unit length lies a distance d from point O as shown in Figure P24.17. Determine the total electric flux through the surface of a sphere of radius R centered at O resulting from this line charge. Consider both cases, where (a) R d and (b) R d.
Suppose the conducting spherical shell of Figure 15.29 carries a charge of 3.00 nC and that a charge of -2.00 nC is at the center of the sphere. If a = 2.00 m and b = 2.40 m. find the electric field at (a) r = 1.50 m, (b) r = 2.20 m, and (c) r = 2.50 m. (d) What is the charge distribution on the sphere?
(a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in Figure 18.53, given that qa= 1.00C and qc=qd= +1.00 C. (b) Calculate the magnitude of the electric field at the location of q, given that the square is 5.00 cm on a side.
Suppose the electric field of Quick Quiz 15.7 is tilted 60 away from the positive z-direction. Calculate the magnitude of the flux through the same area. (a) 0 (b) 10.0 N m2/C (c) 20.0 N m2/C (d) More information is needed
A 10cm10cm piece of aluminum foil of 0.1 mm thickness has a charge of that spreads on both wide side surfaces evenly. You may ignore the charges on the thin sides of the edges. (a) Find the charge density. (b) Find the electric field 1 cm from the center, assuring approximate planar symmetry.
Suppose the electric field of Quick Quiz 15.7 is tilted 60 away from the positive z-direction. Calculate the magnitude of the flux through the same area. (a) 0 (b) 10.0 N m2/C (c) 20.0 N m2/C (d) More information is needed
The electric field everywhere on the surface of a thin, spherical shell of radius 0.750 m is of magnitude 890 N/C and points radially toward the center of the sphere. (a) What is the net charge within the spheres surface? (b) What is the distribution of the charge inside the spherical shell?
Discuss how to orient a planar surface of area A in a uniform electric field of magnitude E0 to obtain (a) the maximum flux and (b) the minimum flux through the area.
Calculate the electric field due to a uniformly charged rod of length L, aligned with the x-axis with one end at the origin; at a point P on the z-axis.
A uniformly charged spherical shell with positive surface charge density contains a circular hole in its surface. The radius r of the hole is small compared with the radius R of the sphere. What is the electric field at the center of the hole? Suggestion: This problem can be solved by using the principle of superposition.
ne electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude 3 N/C and directed outward from the axis of the rod. (a) How much charge per unit length exists on the rod? (b) What would be the electric flux through a cube of side 5 cm situated such that the rod passes through opposite sides of the cube perpendicularly?

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7. Consider the following contour C made of two semi- circles: y Lox (2d,0) (-2d,0) Evaluate the contour integral E ds, if E is a constant electric field given by (a) E = and (b) E = (0, E). (Hint: Make use of the fact that the electric field is a conservative field.)