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Chapter 17: Problem 34

Draw some electric field lines and a few equipotential surfaces outside a negatively charged hollow conducting sphere. What shape are the equipotential surfaces?

Short Answer

Expert verified
Answer: The equipotential surfaces outside a negatively charged hollow conducting sphere are spherical in shape and centered on the sphere itself.

Step by step solution

01

Draw the sphere and its electric field lines

Begin by drawing a negatively charged hollow conducting sphere. Electric field lines around the sphere should point inward, towards the negatively charged surface of the sphere. The lines should be evenly spaced around the sphere.
02

Determine the direction of equipotential surfaces

Recall that equipotential surfaces are always perpendicular to the electric field lines. Therefore, equipotential surfaces around the negatively charged sphere will be centered on the sphere and have a spherical shape.
03

Draw equipotential surfaces

Start with one equipotential surface close to the sphere, with a spherical shape centered on the sphere. As you move further away from the sphere, draw additional equipotential surfaces with a larger radius than the previous surface. These surfaces should also maintain a spherical shape and be centered on the sphere.
04

Analyze the shape of the equipotential surfaces

As we can see from steps 2 and 3, the equipotential surfaces around the negatively charged hollow conducting sphere have a spherical shape, centered on the negatively charged sphere. In conclusion, the equipotential surfaces outside a negatively charged hollow conducting sphere are spherical in shape and centered on the sphere itself.

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Most popular questions from this chapter

A certain capacitor stores \(450 \mathrm{J}\) of energy when it holds $8.0 \times 10^{-2} \mathrm{C}$ of charge. What is (a) the capacitance of this capacitor and (b) the potential difference across the plates?
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(a) Calculate the capacitance per unit length of an axon of radius $5.0 \mu \mathrm{m} \text { (see Fig. } 17.14) .$ The membrane acts as an insulator between the conducting fluids inside and outside the neuron. The membrane is 6.0 nm thick and has a dielectric constant of \(7.0 .\) (Note: The membrane is thin compared with the radius of the axon, so the axon can be treated as a parallel plate capacitor.) (b) In its resting state (no signal being transmitted), the potential of the fluid inside is about \(85 \mathrm{mV}\) lower than the outside. Therefore, there must be small net charges \(\pm Q\) on either side of the membrane. Which side has positive charge? What is the magnitude of the charge density on the surfaces of the membrane?
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