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Ch 25: The Electric Potential
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 25: The Electric PotentialProblema 65
Capitolo 25, Problema 65

Two spherical drops of mercury each have a charge of 0.10 nC and a potential of 300 V at the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop?

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1
Determine the relationship between the charge, potential, and radius of a spherical conductor. The potential at the surface of a spherical conductor is given by the formula: V = kqr, where k is Coulomb's constant, q is the charge, and r is the radius of the sphere.
Calculate the radius of each original drop using the given potential and charge. Rearrange the formula for potential to solve for radius: r = kqV. Substitute the given values for q and V.
Determine the total charge of the new drop after the two drops merge. Since charge is conserved, the total charge is the sum of the charges of the two original drops: q_{total} = q_1 + q_2.
Calculate the radius of the new drop. When two spherical drops merge, the volume is conserved. The volume of a sphere is given by V = 43πr^3. Set the total volume of the two original drops equal to the volume of the new drop and solve for the new radius: r_{new} = (21r_{original}^3)^{1/3}.
Calculate the potential at the surface of the new drop using the formula for potential: V_{new} = kq_{total}r_{new}. Substitute the total charge and the new radius into the formula to find the potential.

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Electric Potential

Electric potential is the amount of electric potential energy per unit charge at a point in an electric field. It is measured in volts (V) and indicates how much work would be done to move a charge from a reference point to a specific point in the field. In this problem, the potential of the mercury drops is crucial for determining the potential of the merged drop.
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Electric Potential

Charge Conservation

Charge conservation is a fundamental principle stating that the total electric charge in an isolated system remains constant over time. When the two mercury drops merge, their individual charges combine to form a single charge for the new drop. This principle is essential for calculating the total charge of the new drop after merging.
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Conservation of Charge

Capacitance of Spheres

The capacitance of a spherical conductor is defined as the ability to store electric charge per unit potential. For a sphere, the capacitance is directly proportional to its radius. When two spherical drops merge, the radius of the new drop changes, affecting its capacitance and, consequently, the potential at its surface, which can be calculated using the relationship between charge, capacitance, and potential.
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Capacitance of Spherical Capacitor
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