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

These are the Notes of Exam of Electromagnetism and Optics which includes Wedge Shaped Conductor, Static Line Charge Density, Rest Frame of Particle, Constant Charge Density etc. Key important points are:Electrostatic Potential, Charge Distribution, Electric Field, Magnetic Induction, Unphysical Vector Field, Integral Relation, Scalar Field

Typology: Exams

2012/2013

Uploaded on 02/11/2013

madangopal
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Physics 110A Midterm 1

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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.