Two small, oppositely charged conducting spheres are to be positioned so that they…

PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance

Problem

Two small, oppositely charged conducting spheres are to be positioned so that they remain just out of contact. Each sphere has a radius of

1.5\,\text{cm}

, and the minimum center-to-center separation therefore equals twice that radius. The charge on the first sphere is fixed at

q_{1}=+6.0\,\mu\text{C}

. The charge

q_{2}

on the second sphere will be adjusted so that, at the minimum separation, the electric potential energy of the system equals

-0.200\,\text{J}

. Neglect any redistribution of charge between the spheres. Use

k=8.99\times10^{9}\,\text{N}\,\text{m}^{2}\,\text{C}^{-2}

. (a) Write a symbolic expression for the electric potential energy of the two-sphere system in terms of

q_{1}

q_{2}

, and the separation

R

. Clearly specify the numerical value of

R

that corresponds to the minimum separation described. (b) Solve algebraically for

q_{2}

in terms of

q_{1}

U

, and

R

. Do not substitute numbers until the end. (c) Determine the required numerical value of

q_{2}

. Express both the magnitude and sign, including appropriate units. (d) State whether the electrostatic interaction between the two spheres at this separation is attractive or repulsive, and explain how the sign of the calculated potential energy supports your conclusion.

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