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(Solved): Q4. Draw a crescent-shaped region R that lies inside the disk D_(1)={(x,y)|(x-2)^(2)+y^(2)<=4} an ...
Q4. Draw a crescent-shaped region
Rthat lies inside the disk
D_(1)={(x,y)|(x-2)^(2)+y^(2)<=4}and outside the disk
D_(2)={(x,y)|(x-1)^(2)+y^(2)<=1}. If the electrostatic potential along the inner circle is kept at 25 volts and the electrostatic potential along the outer circle is kept at 50 volts, then the electrostatic potential at any point
(x,y)in the region
Ris given by
\phi (x,y)=75-(100x)/(x^(2)+y^(2)) volts. i. Compute
\phi _(x)(5,2)and
\phi _(y)(5,2), and interpret your results. ii. Justify whether or not the electrostatic potential
\phi (x,y)is harmonic in the
xy-plane.
