Two metal spheres A and B with radii RA and RB rest far away from one another but are connected by a long wire with a switch. With the switch disconnected, only sphere A is charged, with an initial charge Q1. a) What is the initial magnitude of the electric field |E₁| at the surface of sphere A? b) What is the initial electric potential V, at the surface of sphere A, assuming V→0 an infinite distance away? c) The switch is now connected and the spheres reach electrostatic equilibrium. In terms of the radii, electric constant, and initial charge, what are the final charges QA and QB on each sphere? Assume the wire can transfer charge but only hold a negligible amount. d) What are the final potentials V₁ and VB at the surfaces of each sphere? e) What are the final electric field magnitudes |EA] and [EB] at the surfaces of each sphere?

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Problem 1
Two metal spheres A and B with radii RA and RB rest far away from one another but are connected by
a long wire with a switch. With the switch disconnected, only sphere A is charged, with an initial charge
Q1.
a) What is the initial magnitude of the electric field |E₁| at the surface of sphere A?
b) What is the initial electric potential V, at the surface of sphere A, assuming V → 0 an infinite distance
away?
c) The switch is now connected and the spheres reach electrostatic equilibrium. In terms of the radii,
electric constant, and initial charge, what are the final charges QA and QB on each sphere? Assume the
wire can transfer charge but only hold a negligible amount.
d) What are the final potentials V₁ and VB at the surfaces of each sphere?
e) What are the final electric field magnitudes |Ē₁] and |ĒB] at the surfaces of each sphere?
Transcribed Image Text:Problem 1 Two metal spheres A and B with radii RA and RB rest far away from one another but are connected by a long wire with a switch. With the switch disconnected, only sphere A is charged, with an initial charge Q1. a) What is the initial magnitude of the electric field |E₁| at the surface of sphere A? b) What is the initial electric potential V, at the surface of sphere A, assuming V → 0 an infinite distance away? c) The switch is now connected and the spheres reach electrostatic equilibrium. In terms of the radii, electric constant, and initial charge, what are the final charges QA and QB on each sphere? Assume the wire can transfer charge but only hold a negligible amount. d) What are the final potentials V₁ and VB at the surfaces of each sphere? e) What are the final electric field magnitudes |Ē₁] and |ĒB] at the surfaces of each sphere?
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