A large aluminum sphere (radius R = 1.0m) is temporarilyconnected by a long, thi

Question

A large aluminum sphere (radius R = 1.0m) is temporarilyconnected by a long, thin, insulated copper wire to a smallaluminum sphere (radius r = 1.0cm). A charge ofQT = 2×10-6 C is placed ontothe system and is shared between the two spheres. The wire is thenremoved. Find the charges Q and q on the largeand small spheres, respectively, and their potentials in volts.What are the field strengths at the surfaces of the large and smallspheres? If we reconnect the thin wire, increase the total chargeQT on the system to 4 ×10-6 C, and then remove the wire, will electrical breakdown in the airadjacent to the spheres occur?

NOTE: Dry air can sustain a maximum electrical fieldstrength of 3×106 V/m .

Explanation / Answer

connected by a long, thin, insulated copper wire large and small ones have the same potential V q1/R=q2/r => q1=100q2 q1+q2=QT q2=1.98*10-8C q1=1.98*10-6C q1=Q q2=q V=k*q/r=17820V (b)field strenth: small E=k*q/r2= 1782000 V/m large E=k*Q/R2=17820 V/m (c) increase the total charge QT onthe system to 4 ×10-6 C q=3.96*10-8 C => Eq=2*1782000 V/m=3564000> 3000000 => electrical breakdown in the air adjacent to thespheres is occurred q2=1.98*10-8C q1=1.98*10-6C q1=Q q2=q V=k*q/r=17820V (b)field strenth: small E=k*q/r2= 1782000 V/m large E=k*Q/R2=17820 V/m (c) increase the total charge QT onthe system to 4 ×10-6 C q=3.96*10-8 C => Eq=2*1782000 V/m=3564000> 3000000 => electrical breakdown in the air adjacent to thespheres is occurred

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