Text: PROBLEM-1 (30 points):
Consider a charged sphere (total charge is Q) with radius R. This sphere has a spherically symmetric charge density (p) and it is given as p (r)=A r where A is constant. Use Gauss's Integral Law to obtain the electric fields both a inside and b) outside of the sphere. c) Bonus (+10 points): Plot the behavior of the fields as a function of radius when n =-2, -1,+1 and +2.
PROBLEM-2(30 points):
Show that Maxwell's equations in vacuum condition can be employed in order to produce the
fields are written as follows Include all work(i.e.show all steps) for one of them is enough!):
E
B B-H at^2
Hints:
Be sure that you are using Maxwell's equations for vacuum condition Start with finding out a relation for Vx(Vx Eby using Maxwell's Equations Use a vector identityVx(VE=VVE-VVE Use VE=O,and the definition of the LaplacianVVE=VE Follow the same procedure for magnetic field.
PROBLEM-3:Some practice questions on Mathematical Identities (40 points)
Show that Show that aScalar Potential (V) bVector PotentialA Curl(Grad(U))=0 Div(Curl(A))=0 Use the following identities while solving a and b parts: A=AAAwhereF=yz V=0x,y,0 c Show that d) Show that x-x 1 -x 7-713 17-713 Then,just generalize it to Then,just generalize it to F-r 7-713 17-T13 Use the following identities while solving c and d parts: F=y.zand=xyandV=y Example V operationx^2=2x=2