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Chapter 23: Q. 1 (page 652)

You’ve been assigned the task of determining the magnitude and direction of the electric field at a point in space. Give a step-by-step procedure of how you will do so. List any objects you will use, any measurements you will make, and any calculations you will need to perform. Make sure that your measurements do not disturb the charges that are creating the field.

Short Answer

Expert verified

Calculate the electric field by $E = \frac{F}{q}$ .

Step by step solution

01

Given information

Given a point in space of electric field.

02

Explanation

To determine the electric field, place a positive test charge which does not disturb the system's configuration.
Measure the force on the test charge.
Electric field at a point is the force experienced by the test charge at that point. From the measured force and charge calculate the electric field using $E = \frac{F}{q}$
Direction of the electric field is the same as the direction of the force on the charge.

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Most popular questions from this chapter

Two $10 cm$ diameter charged rings face each other, $20 cm$ apart. Both rings are charged to $+ 20 nC$ . What is the electric field strength at (a) the midpoint between the two rings and (b) the center of the left ring?

An electric dipole is formed from two charges, $\pm q$ , spaced $1.0 c m$ apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point $(x, y) = (0 c m, 10 c m)$ is $360 N / C$ .

a. What is the charge q? Give your answer in $n C$ .

b. What is the electric field strength at the point $(x, y) = (10 c m, 0 c m)$ ?

You have a summer intern position with a company that designs and builds nanomachines. An engineer with the company is designing a microscopic oscillator to help keep time, and you’ve been assigned to help him analyze the design. He wants to place a negative charge at the center of a very small, positively charged metal ring. His claim is that the negative charge will undergo simple harmonic motion at a frequency determined by the amount of charge on the ring.

a. Consider a negative charge near the center of a positively charged ring centered on the $z - a x i s$ . Show that there is a restoring force on the charge if it moves along the $z - a x i s$ but stays close to the center of the ring. That is, show there’s a force that tries to keep the charge at $z = 0$ . b. Show that for small oscillations, with amplitude $< < R$ , a particle of mass $m$ with charge $- q$ undergoes simple harmonic motion with frequency $f = \frac{1}{2 π} \sqrt{\frac{q Q}{4 π ε_{0} m R^{3}}}$ , $R and Q$ are the radius and charge of the ring.

c. Evaluate the oscillation frequency for an electron at the center of a $2.0 μ m$ diameter ring charged to $1.0 \times 10^{- 13} C$ .

A $20 cm \times 20 cm$ horizontal metal electrode is uniformly charged to $+ 80 nC$ . What is the electric field strength $2.0 mm$ above the center of the electrode?

Show that an infinite line of charge with linear charge density $λ$ exerts an attractive force on an electric dipole with magnitude $F = \frac{2 λ p}{4 π ε_{0} r^{2}}$ . Assume that $r$ , the distance from the line, is much larger than the charge separation in the dipole.

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