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Chapter 23: Problem 37

A spherical water drop \(50.0 \mu \mathrm{m}\) in diameter has a uniformly distributed charge of \(+20.0 \mathrm{pC}\). Find (a) the potential at its surface and (b) the potential at its center.

Short Answer

Expert verified
Answer: The potential at both the surface and the center of the water drop is 7192 volts.

Step by step solution

01

Identify given values

We are given the diameter (\(50.0 \mu m\)) of the water drop, and its charge (\(+20.0 pC\)). Let's convert these values to meters and Columbs respectively: Diameter = \(50.0 \mu m = 50.0 × 10^{-6} m\) Charge = \(+20.0 pC = 20.0 × 10^{-12} C\)
02

Find the radius of the water drop

To find the radius of the water drop, divide the diameter in meters by 2: Radius = \(\frac{50.0 × 10^{-6} m}{2} = 25.0 × 10^{-6} m\)
03

Calculate potential at the surface

Use the formula for potential to find the potential at the surface of the charged sphere: \(V_{surface} = \frac{kQ}{r}\) \(V_{surface} = \frac{8.99 × 10^9 Nm^2 C^{-2} × 20.0 × 10^{-12} C}{25.0 × 10^{-6} m}\) \(V_{surface} = 7192 V\) The potential at the surface of the water drop is 7192 volts.
04

Calculate potential at the center

For a uniformly charged sphere, the potential at the center is equal to the potential at the surface (since the electric field inside is zero). So the potential at the center is: \(V_{center} = V_{surface}\) \(V_{center} = 7192 V\) The potential at the center of the water drop is also 7192 volts.

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Most popular questions from this chapter

A proton is placed midway between points \(A\) and \(B\). The potential at point \(A\) is \(-20 \mathrm{~V}\), and the potential at point \(B\) \(+20 \mathrm{~V}\). The potential at the midpoint is \(0 \mathrm{~V}\). The proton will a) remain at rest. b) move toward point \(B\) with constant velocity. c) accelerate toward point \(A\). d) accelerate toward point \(B\). e) move toward point \(A\) with constant velocity.

A classroom Van de Graaff generator accumulates a charge of \(1.00 \cdot 10^{-6} \mathrm{C}\) on its spherical conductor, which has a radius of \(10.0 \mathrm{~cm}\) and stands on an insulating column. Neglecting the effects of the generator base or any other objects or fields, find the potential at the surface of the sphere. Assume that the potential is zero at infinity.

Two parallel plates are held at potentials of \(+200.0 \mathrm{~V}\) and \(-100.0 \mathrm{~V}\). The plates are separated by \(1.00 \mathrm{~cm}\). a) Find the electric field between the plates. b) An electron is initially placed halfway between the plates. Find its kinetic energy when it hits the positive plate.

High-voltage power lines are used to transport electricity cross country. These wires are favored resting places for birds. Why don't the birds die when they touch the wires?

How much work would be done by an electric field in moving a proton from a point at a potential of \(+180 . \mathrm{V}\) to a point at a potential of \(-60.0 \mathrm{~V} ?\)
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