Physics 241 Lab – Matt Leone TEST 1 REVIEW - REVISED [email protected] (email preferred), PAS 376, o. 520-621-6819 Office Hours: M & W 11:00-11:50, or by appointment. Consultation Room (PAS 372): F 12:00-12:50 http://bohr.physics.arizona.edu/~leone/phy241/phys241lab.html GAUSS’ LAW – A TARGETED REVIEW 1. Review single point charge. 2. Review spherical shell with uniform surface charge density. 3. Review solid sphere with uniform volume charge density. 4. PROBLEM A – A solid insulating sphere of radius R is centered at the origin and has an uncharged hollow spherical cavity with radius B also centered at the origin. Clearly R>B. The total uniform charge on the spherical shell is Q. a. What is the uniform volume charge density of the hollow sphere? b. What is the electric field for r > R? c. What is the electric field for R > r > B? d. What is the electric field for r < B? e. What is the electric field for r = R? 5. Review infinite line of charge. 6. Review infinite cylindrical shell with uniform surface charge density. 7. PROBLEM B – An infinite cylinder of radius R lies with its center on the z-axis with uniform volume charge density, ρ. a. What is the electric field for r > R? b. What is the electric field for r = R? c. What is the electric field for r < R? d. What is the electric field for r = 0? 8. Review infinite plane of charge. 9. PROBLEM C – An infinite plane with uniform surface charge density σ, is parallel to the x-z plane and passes through the y-axis at 2 m. a. What is the electric field at the point (4 m, -7 m, 0 m)? b. What is the electric field for y > 2 m?10. PROBLEM D – An infinite plane with uniform surface charge density σ, is parallel to the x-z plane and passes through the y-axis at 2 m. Another infinite plane with uniform surface charge density -2σ, is parallel to the x-z plane and passes through the y-axis at 3 m. a. What is the electric field for y < 2 m? b. What is the electric field for 2 m < y < 3 m? c. What is the electric field for y > 3 m? 11. PROBLEM E – An infinite plane with uniform surface charge density σ, is parallel to the x-y plane and passes through the z-axis at -2 m. A spherical shell with radius 1 m and uniform surface charge density -2σ is centered at ( 0, 0, 2). a. What is the electric field at ( 0, 0, 0)? CONDUCTORS – A TARGETED REVIEW (USING GAUSS’ LAW) 12. Review THE basic property of conductors. Einside = 0. a. Q-charged solid conducting sphere. b. Q-charged solid conducting sphere with empty cavity. c. Q-charged solid conducting sphere with cavity; cavity has q inside. 13. PROBLEM F – A solid conducting sphere of radius R is centered at the origin and has a hollow spherical cavity with radius B also centered at the origin. Clearly R > B. This is often called a spherical conducting shell. The total charge of the spherical conducting shell is Q. At the origin sits a point charge of q. a. What is the electric field at r > R? b. What is the electric field at R > r > B? c. What is the electric field at B > r > 0? d. What is the electric field at r = 0? e. What is the total charge on the inner surface of the sphere and what is its uniform surface density, σinside. f. What is the total charge on the outer surface of the sphere and what is its uniform surface density, σoutside. g. In which case will σoutside have the largest positive value: a) Q > 0, q < 0 OR b) Q > 0, q > 0. Use a picture to explain why.14. More review of conductors. a. σ-charged infinite solid conducting cylinder. b. σ-charged infinite solid conducting cylinder with hollow infinite cylindrical cavity inside. 15. PROBLEM G – An infinite conducting cylindrical shell has outer radius R and inner radius B and is centered along the z-axis. Clearly R > B. The total linear charge density on the infinite conducting cylindrical shell is λ. Along the z-axis is an infinite line of charge with linear density -λ. a. What is the total uniform linear charge density, λinside, on the inner surface of the cylindrical shell. b. What is the total uniform linear charge density, λoutside, on the outer surface of the cylindrical shell. c. What is the electric field at r > R? d. What is the electric field at R > r > B? e. What is the electric field at B > r > 0? f. What is the electric field at r = 0? 16. PROBLEM H – An infinite conducting slab of width W is parallel to the x-z plane and passes through the origin. An infinite plane with uniform surface charge density σ, is also parallel to the x-z plane and passes through the y-axis at 3 m. Clearly W/2 < 3. The total surface charge density of the infinite conducting slab is also σ. a. What is the total uniform surface charge density, σ-W/2, on the surface of the slab at y = -W/2? b. What is the total uniform surface charge density, σ+W/2, on the surface of the slab at y = +W/2? c. What is the electric field at y < -W/2? d. What is the electric field at –W/2 < y < +W/2? e. What is the electric field at +W/2 < y < 3? f. What is the electric field at y >
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