Electrostatic Potential - Electromagnetism and Optics - Exam, Exams of Electromagnetism and Electromagnetic Fields Theory

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• Physics 110A Midterm

Physics 110A Midterm 1 . wa ro - - . Given a charge distribution: p = "7 forr $a and zero [or r >a (po is a constant), a. Find the electric field inside and outside the sphere. b. Find the electrostatic potential inside and outside the sphere. Take the potential = 0 as 1 infinity. (Be sure your potential is continuous at r = a!) 2. An infinitely long wire carries a current I. It is bent so as to have a semicircular detour around the origin, with radius R. Calculate the magnetic induction (B) at the origin. a Re : —_______ ne 3. Consider the a completely crazy unphysical vector field given by: Cir) = Jee Rav’ Where R=r—r’ : a. Show that C(r) = V(r): where y(r) is a scalar field and write an integral relation for ydr) in terms of afr’). b. Find V-Cqr) (Note: it is a constant (i.e. the same at all r) independent of the form of a(r’)). ¢. For at) = a, for rb: calculate V»C at all r. 6, Calculate C(t) at all. 4. A sphere of radius a has a uniform yolume charge density p except for a sphcrical cavity of radius c, at a distance of b from the center of the sphere, where the charge density is zero. Hint this problem is about superposition. You may use the standard result for the electric field inside a uniform charged sphere: Ea oF and Vry= Pp where V=0 at r=0 3e, 6&, Find expressions for the eleciric field and the potential anywhere in the cavity. It is your choice, which you find first. Just be sure that they are mutually consistent.