ssm_ch22 - Chapter 22 3 Since the magnitude of the electric...

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Chapter 22 3 Since the magnitude of the electric field produced by a point particle with charge q is given by E = j q j = 4 ¼² 0 r 2 ,whe re r is the distance from the particle to the point where the field has magnitude E , the magnitude of the charge is j q j =4 ¼² 0 r 2 E = (0 : 50 m) 2 (2 : 0N = C) 8 : 99 £ 10 9 N ¢ m 2 = C 2 =5 : 6 £ 10 ¡ 11 C : 5 Since the charge is uniformly distributed throughout a sphere, the electric field at the surface is exactly the same as it would be if the charge were all at the center. That is, the magnitude of the field is E = q 4 ¼² 0 R 2 ; where q is the magnitude of the total charge and R is the sphere radius. The magnitude of the total charge is Ze ,so E = Ze 4 ¼² 0 R 2 = (8 : 99 £ 10 9 N ¢ m 2 = C 2 )(94)(1 : 60 £ 10 ¡ 19 C) (6 : 64 £ 10 ¡ 15 m) 2 =3 : 07 £ 10 21 N = C : The field is normal to the surface and since the charge is positive it points outward from the surface. 9 Choose the coordinate axes as shown on the diagram to the right. At the center of the square, the electric fields produced by the particles at the lower left and upper right corners are both along the x axis and each points away from the center and toward the particle that produces it. Since each particle is a distance d = p 2 a= 2= a= p 2 away from the center, the net field due to these two particles is E x = 1 4 ¼² 0 2 q a 2 = 2 ¡ q a 2 = 2 ¸ ² ² ² ² . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d d a a x y ¡ q q ¡ 2 q 2 q = 1 4 ¼² 0 q a 2 = 2 = (8 : 99 £ 10 9 N ¢ m 2 = C 2 )(1 : 0 £ 10 ¡ 8 C) (0 : 050 m) 2 = 2 =7 : 19 £ 10 4 N = C. Chapter 22
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At the center of the square, the field produced by the particles at the upper left and lower right corners are both along the y axis and each points away from the particle that produces it. The net field produced at the center by these particles is E y = 1 4 ¼² 0 2 q a 2 = 2 ¡ q
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ssm_ch22 - Chapter 22 3 Since the magnitude of the electric...

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