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PHYS 196 Home Work 3B (Gauss Law) 1. A uniform electric field of magnitude 720N/C passes through a circular disk of radius 13cm . Find the electric flux if its face is (a) perpendicular to the field line, (b) at 30 to the field line, and (c) parallel to the field line. 2. A uniform electric field E is parallel to the axis of a hollow hemisphere of radius r . (a) What is the electric flux through the hemispherical surface? (b) What is the result if E is perpendicular to the axis? 3. A point charge q is at the center of a cube of side a . What is the electric flux through one of the faces? 4. A spherical shell of radius 25cm has a surface charge density 48nC / m 2 . Find the electric field at a point (a) just outside the surface, (b) in the interior, and (c) at a distance 50cm from the center. 5. A solid sphere of radius 25cm carries a total charge 72nC uniformly distributed over its volume. Find the electric field (a) at a point just outside the sphere, and (b) at an interior point 10cm from the center. 6. Two concentric thin spherical shells of radius R1 and R2 with R1 R2 carry uniformly distributed charge Q1 and Q2 respectively. Use Gauss law to find the electric field at a point a distance r from the center, in the three cases r R2 , R2 r R1 and R1 r . 7. A solid sphere of radius a carries a uniform charge distribution over its volume. The total charge is Q . Use Gauss law to find the electric field at a point a distance r from the center in the two cases r a and ra. 8. Two coaxial infinitely long thin cylindrical shells of radius R1 and R2 with R1 R2 carry uniformly distributed charge per unit length of 1 and 2 respectively. Use Gauss law to find the electric field at a point a distance r from the axis, in the three cases r R2 , R2 r R1 and R1 r . 9. From a solid sphere of radius a with a uniform charge density , a spherical volume of radius a 2 is removed as shown. Find the magnitude and direction of the electric field at the center of the original sphere. 10. The electron cloud in a hydrogen atom corresponds to a spherically symmetric charge distribution with volume charge density 0e 2 r a where r is the distance from the center. Find the electric field as a function of r . 1 Answers: Q 1 Qr , 2 40 r 40 a 3 1 1 2 1 1 , , 0 8. 20 r 20 r a 9. 6 0 1. 38.2 Nm2 / C, 19.1Nm2 / C, 0 7. 2. r 2 E , 0 3. q 6 0 1 0 a 3 2r 2 2r 2 r a 1e 10. 1 4 0 r 2 a 2 a 4. 5400 N / C , 0, 1350 N / C 5. 1.04 104 N / C, 4140 N / C 1 Q1 Q2 1 Q1 , , 0 6. 2 40 r 40 r 2 2