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Chapter 17: Problem 60

A shark is able to detect the presence of electric fields as small as $1.0 \mu \mathrm{V} / \mathrm{m} .$ To get an idea of the magnitude of this field, suppose you have a parallel plate capacitor connected to a 1.5 - \(V\) battery. How far apart must the parallel plates be to have an electric field of $1.0 \mu \mathrm{V} / \mathrm{m}$ between the plates?

Short Answer

Expert verified
Answer: The distance between the parallel plates must be 1.5 x 10^6 meters.

Step by step solution

01

Write down the formula for electric field in a parallel plate capacitor

The electric field in a parallel plate capacitor can be calculated using the following formula: \(E = \frac{V}{d}\) where \(E\) is the electric field, \(V\) is the voltage, and \(d\) is the distance between the plates.
02

Plug in the given values

We are given the electric field \(E = 1.0 \mu \mathrm{V} / \mathrm{m}\) and the voltage \(V = 1.5 \, \mathrm{V}\). We can plug these values into the formula: \(1.0 \times 10^{-6} \, \mathrm{V/m} = \frac{1.5 \, \mathrm{V}}{d}\)
03

Solve for the distance \(d\)

Now we need to solve for \(d\): \(d = \frac{1.5 \, \mathrm{V}}{1.0 \times 10^{-6} \, \mathrm{V/m}}\)
04

Calculate the distance

Multiply both the numerator and denominator: \(d = \frac{1.5}{1.0 \times 10^{-6}} \, \mathrm{m}\) \(d = 1.5 \times 10^{6} \, \mathrm{m}\)
05

Write the final answer

The distance between the parallel plates must be \(1.5\times 10^{6}\) meters to have an electric field of \(1.0 \mu \mathrm{V/m}\).

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Most popular questions from this chapter

A tiny hole is made in the center of the negatively and positively charged plates of a capacitor, allowing a beam of electrons to pass through and emerge from the far side. If \(40.0 \mathrm{V}\) are applied across the capacitor plates and the electrons enter through the hole in the negatively charged plate with a speed of \(2.50 \times 10^{6} \mathrm{m} / \mathrm{s}\) what is the speed of the electrons as they emerge from the hole in the positive plate?
An alpha particle (helium nucleus, charge \(+2 e\) ) starts from rest and travels a distance of \(1.0 \mathrm{cm}\) under the influence of a uniform electric field of magnitude \(10.0 \mathrm{kV} / \mathrm{m}\) What is the final kinetic energy of the alpha particle?
Capacitors are used in many applications where you need to supply a short burst of energy. A \(100.0-\mu \mathrm{F}\) capacitor in an electronic flash lamp supplies an average power of \(10.0 \mathrm{kW}\) to the lamp for $2.0 \mathrm{ms}$. (a) To what potential difference must the capacitor initially be charged? (b) What is its initial charge?
A parallel plate capacitor has a capacitance of \(1.20 \mathrm{nF}\) There is a charge of \(0.80 \mu \mathrm{C}\) on each plate. How much work must be done by an external agent to double the plate separation while keeping the charge constant?
A 200.0 - \(\mu\) F capacitor is placed across a \(12.0-\mathrm{V}\) battery. When a switch is thrown, the battery is removed from the capacitor and the capacitor is connected across a heater that is immersed in $1.00 \mathrm{cm}^{3}$ of water. Assuming that all the energy from the capacitor is delivered to the water, what is the temperature change of the water?
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