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Chapter 22: Problem 38

Research suggests that the electric fields in some thunderstorm clouds can be on the order of \(10.0 \mathrm{kN} / \mathrm{C}\). Calculate the magnitude of the electric force acting on a particle with two excess electrons in the presence of a \(10.0-\mathrm{kN} / \mathrm{C}\) field.

Short Answer

Expert verified
Answer: The magnitude of the electric force acting on the particle is approximately 3.2 × 10^{-15} N.

Step by step solution

01

Identify the given values

In this problem, we are given: - Electric field strength E: 10.0 kN/C - Number of excess electrons: 2
02

Convert the electric field strength to standard units

The electric field strength is given in kN/C. To convert it into the standard unit of N/C, we will multiply by 1000: E = 10.0 kN/C × 1000 = 10,000 N/C
03

Determine the charge of the particle

Since the particle has two excess electrons, we will calculate the charge of the particle by multiplying the charge of one electron by the number of excess electrons. The charge of one electron (e) is approximately -1.6 × 10^{-19} C: Charge (q) = Number of excess electrons × Charge of one electron = 2 × (-1.6 × 10^{-19} C)
04

Calculate the electric force

The electric force (F) acting on the particle is the product of the electric field strength (E) and the charge of the particle (q): F = E × q Substitute the values of E and q from the previous steps: F = (10,000 N/C) × (2 × -1.6 × 10^{-19} C) Now, perform the calculation to obtain the electric force: F ≈ -3.2 × 10^{-15} N The negative sign indicates that the force is in the opposite direction of the electric field. In conclusion, the magnitude of the electric force acting on the particle with two excess electrons in the presence of a 10.0 kN/C electric field is approximately 3.2 × 10^{-15} N.

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Most popular questions from this chapter

An electron is observed traveling at a speed of \(27.5 \cdot 10^{6} \mathrm{~m} / \mathrm{s}\) parallel to an electric field of magnitude \(11,400 \mathrm{~N} / \mathrm{C}\) How far will the electron travel before coming to a stop?

Two uniformly charged insulating rods are bent in a semicircular shape with radius \(r=10.0 \mathrm{~cm} .\) If they are positioned so they form a circle but do not touch and have opposite charges of \(+1.00 \mu \mathrm{C}\) and \(-1.00 \mu \mathrm{C}\) find the magnitude and direction of the electric field at the center of the composite circular charge configuration.

An infinitely long, solid cylinder of radius \(R=9.00 \mathrm{~cm},\) with a uniform charge per unit of volume of \(\rho=6.40 \cdot 10^{-8} \mathrm{C} / \mathrm{m}^{3},\) is centered about the \(y\) -axis. Find the magnitude of the electric field at a radius \(r=4.00 \mathrm{~cm}\) from the center of this cylinder.

A long conducting wire with charge distribution \(\lambda\) and radius \(r\) produces an electric field of \(2.73 \mathrm{~N} / \mathrm{C}\) just outside the surface of the wire. What is the magnitude of the electric field just outside the surface of another wire with charge distribution \(0.81 \lambda\) and radius \(6.5 r ?\)

Carbon monoxide (CO) has a dipole moment of approximately \(8.0 \cdot 10^{-30} \mathrm{C} \mathrm{m} .\) If the two atoms are separated by \(1.2 \cdot 10^{-10} \mathrm{~m}\), find the net charge on each atom and the maximum amount of torque the molecule would experience in an electric field of \(500.0 \mathrm{~N} / \mathrm{C}\).
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