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Review Pt I Problems

# Review Pt I Problems - Physics 7B, Fall 2010, Midterm...

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Unformatted text preview: Physics 7B, Fall 2010, Midterm Review, 10/30/2010 Raj Misra ([email protected]) A thin ring of charge. Déjà vu? But, this time with a non uniform charge density. (Irodov). A thin ring of non ­conducting charge of radius R has a linear charge density λ = λ0 cos ϕ , where λ0 is a constant, ϕ is the azimuthal angle. Find the electric field and potential at the center of the ring. Take the potential at infinity to be 0. Problem 1 1 Physics 7B, Fall 2010, Midterm Review, 10/30/2010 Raj Misra ([email protected]) Given the electric potential, find the charge density (Irodov). The electric potential inside a ball of charge depends only on the radial distance r from its center. Specifically, it is given by Φ(r ) = ar 2 + b , where a and b are constants. Find the volume charge density ρ (r) inside the ball. Problem 2 2 Physics 7B, Fall 2010, Midterm Review, 10/30/2010 Raj Misra ([email protected]) Think concepts (adapted from MT2, Professor Jacobsen). 1. In a certain picture two electric field lines cross at a point. Does it mean (a) two charges are present (b) a conductor exists at the point of intersection (c) equipotential surface has collapsed to a point (d) this picture is physically impossible (e) the electric field correctly points in two directions at that point. 2. Which of the charges q1, q2, and q3 contribute to the electric flux through the shaded Gaussian surface? Which charges contribute to the electric field at a point on this Gaussian surface? Problem 3 3. Does zero enclosed charge imply zero electric field at a closed surface? Does zero electric field at a surface imply zero enclosed charge? Give examples. 4. Find the force on charge q inside the conducting spherical shell and on charge Q outside. Are they equal and opposite? If not, what about Newton’s third law? (Please ignore the letters ‘ng’ in this figure). 3 Physics 7B, Fall 2010, Midterm Review, 10/30/2010 Raj Misra ([email protected]) Two distant ball bearings make one cool capacitor (Irodov). Find the capacitance of a system of two identical metal balls of radius a, separated by a distance b >> a. The entire arrangement is immersed in a dielectric medium with dielectric constant K. Hint: How does the assumption b >> a, effect the charge distribution on each ball? Problem 4 4 Physics 7B, Fall 2010, Midterm Review, 10/30/2010 Raj Misra ([email protected]) Potential of two conducting spheres, again? (Irodov). A system consists of two concentric conducting spheres, with inside sphere of radius a, charge q1. What charge must be placed on the outside sphere of radius b to reduce the potential on the inside sphere to zero? How does the potential and electric field of the system vary with distance r from the center? Problem 5 5 Physics 7B, Fall 2010, Midterm Review, 10/30/2010 Raj Misra ([email protected]) Electric field at work expands a sphere (Irodov). A spherical shell of radius R1 with uniformly distributed charge q expands to radius R2. Find the work performed by the electric field in the process. Problem 6 6 Physics 7B, Fall 2010, Midterm Review, 10/30/2010 Raj Misra ([email protected]) Problem 7 A particle gains kinetic energy…(Final exam, Professor Liphardt). An infinitely long, non ­conducting cylinder has thickness r2 r1 and a volume charge density ρ . It is positioned a distance d above an infinite non ­conducting sheet with uniform surface charge density σ . A particle of mass m and charge –q is released from point a, at a height l above the cylinder. What is the kinetic energy of the particle when it collides with the cylinder? m 2: (20 a . An infinitely non-conducting r has thickness The cylinder has iform volume density ! and is ed a distance d rom an infinite nducting sheet surface charge ". A charged ge -q) is released from point a, at a height l above the cylinder. (mass m and char s the kinetic energy of the particle when it collides with the cylinder? Neglect . 7 Physics 7B, Fall 2010, Midterm Review, 10/30/2010 Raj Misra ([email protected]) Make it compact. Is there a limit to the energy density of a practical capacitor? Analyze using a parallel pale capacitor. Problem 8 8 Physics 7B, Fall 2010, Midterm Review, 10/30/2010 Raj Misra ([email protected]) Potential in the plane of a disk (Irodov). Problem 9 A thin disk of radius R carries a uniform surface charge density σ . Find the potential at a point located at its edge. 9 ...
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