A +8.75+8.75-mC point charge is glued down on a horizontal frictionless table. It is tied to a −6.50-6.50-mC point charge by a light, nonconducting 2.502.50-cm wire. A uniform electric field of magnitude 1.85×1081.85\$$times10^8 N/CN/C is $$directed parallel to the wire, as shown in Fig. E21.3421.34. Find the tension in the wire.

Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 21: Electric Charge and Electric Field

Problem 34a

Chapter 21, Problem 34a

A $positive 8.75$ -mC point charge is glued down on a horizontal frictionless table. It is tied to a $negative 6.50$ -mC point charge by a light, nonconducting $2.50$ -cm wire. A uniform electric field of magnitude $1.85 \times 10^{8}$ $N / C$ is directed parallel to the wire, as shown in Fig. E $21.34$ . Find the tension in the wire.

Verified step by step guidance

Identify the forces acting on the charges. The positive charge experiences a force due to the electric field and the negative charge experiences a force due to the electric field in the opposite direction.

Calculate the force on each charge due to the electric field using the formula: F = qE, where q is the charge and E is the electric field magnitude.

Determine the force between the two charges using Coulomb's law: F = k * |q1 * q2| / r^2, where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.

Consider the direction of the forces. The electric field force on the positive charge is in the direction of the field, while the force on the negative charge is opposite to the field direction. The Coulomb force is attractive, pulling the charges together.

Set up the equilibrium condition for the wire. The tension in the wire must balance the net force on each charge, which is the sum of the electric field force and the Coulomb force. Solve for the tension in the wire.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Coulomb's Law

Coulomb's Law describes the electrostatic force between two point charges. The force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This force is attractive if the charges are of opposite signs and repulsive if they are of the same sign.

Electric Field

An electric field is a vector field around a charged object where a force would be exerted on other charges. The field's strength is measured in newtons per coulomb (N/C) and is defined as the force per unit charge. In this problem, the uniform electric field affects the charges, contributing to the tension in the wire.

Tension in a Wire

Tension in a wire is the force exerted along the wire, which in this scenario is due to the electrostatic forces between the charges and the external electric field. The tension must balance these forces to maintain equilibrium, and it can be calculated by considering the net force acting on the system of charges.

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Textbook Question

A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, $1.60$ cm distant from the first, in a time interval of $3.20 \times 10^{- 6}$ s. Find the magnitude of the electric field.

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Textbook Question

Two positive point charges $q$ are placed on the $x$ -axis, one at $x = a$ and one at $x = -a$ . Derive an expression for the electric field at points on the $x$ -axis. Use your result to graph the $x$ -component of the electric field as a function of $x$ , for values of $x$ between $negative 4 a$ and $positive 4 a$ .

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Textbook Question

A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, $1.60$ cm distant from the first, in a time interval of $3.20$\times$10^{-6}$ s. Find the speed of the proton when it strikes the negatively charged plate.

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Textbook Question

Calculate the magnitude and direction (relative to the $+ x$ -axis) of the electric field in Example $21.6$ . Example $21.6$ : A point charge $q = - 8.0$ nC is located at the origin. Find the electric-field vector at the field point $x equals 1.2$ m, $y = - 1.6$ m.

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Textbook Question

A $+8.75$ -mC point charge is glued down on a horizontal frictionless table. It is tied to a $-6.50$ -mC point charge by a light, nonconducting $2.50$ -cm wire. A uniform electric field of magnitude $1.85$\times$10^8$ $N/C$ is directed parallel to the wire, as shown in Fig. E $21.34$ . What would the tension be if both charges were negative?

3310

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Textbook Question

Two positive point charges $q$ are placed on the $x$ -axis, one at $x = a$ and one at $x = - a$ . Find the magnitude and direction of the electric field at $x equals 0$ .

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