Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 21: Electric Charge and Electric Field

Problem 40b

Chapter 21, Problem 40b

A $negative 4.00$ -nC point charge is at the origin, and a second $-5.00$ -nC point charge is on the $x$ -axis at $x = 0.800$ m. Find the net electric force that the two charges would exert on an electron placed at each point in part (a). Note: Part (a) asked to find the electric field (magnitude and direction) at each of the following points on the $x$ -axis: (i) $x = 0.200$ m; (ii) $x = 1.20$ m; (iii) $x = -0.200$ m.

Verified step by step guidance

To find the electric field at a point due to a point charge, use the formula: E = (k * |q|) / r^2, where E is the electric field, k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), q is the charge, and r is the distance from the charge to the point.

For point (i) x = 0.200 m, calculate the electric field due to each charge separately. For q1 at the origin, r = 0.200 m. For q2 at x = 0.800 m, r = 0.600 m. Determine the direction of each field: both charges are negative, so the electric field points towards the charges.

For point (ii) x = 1.20 m, calculate the electric field due to each charge. For q1, r = 1.20 m. For q2, r = 0.400 m. Again, determine the direction of each field: both fields point towards the charges.

For point (iii) x = -0.200 m, calculate the electric field due to each charge. For q1, r = 0.200 m. For q2, r = 1.000 m. Determine the direction of each field: both fields point towards the charges.

To find the net electric force on an electron at each point, use F = e * E, where e is the charge of an electron (1.60 x 10^-19 C). Calculate the force using the net electric field found at each point.

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Key Concepts

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

Electric Field

The electric field is a vector field around a charged particle that represents the force exerted per unit charge at any point in space. It is calculated using Coulomb's law, where the electric field E due to a point charge q at a distance r is given by E = k * |q| / r^2, with k being Coulomb's constant. The direction of the field is radially outward for positive charges and inward for negative charges.

Superposition Principle

The superposition principle states that the net electric field due to multiple charges is the vector sum of the electric fields produced by each charge individually. This principle allows us to calculate the total electric field at a point by considering the contribution from each charge separately and then adding them together, taking into account both magnitude and direction.

Electric Force on a Charge

The electric force on a charge in an electric field is given by F = qE, where F is the force, q is the charge, and E is the electric field at the location of the charge. For an electron, which has a negative charge, the direction of the force is opposite to the direction of the electric field. This concept is crucial for determining the net force on a charge placed in the vicinity of other charges.

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Related Practice

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 point charge $q_{1} = - 4.00$ nC is at the point $x equals 0.600$ m, $y equals 0.800$ m, and a second point charge $q sub 2 equals positive 6.00$ nC is at the point $x equals 0.600$ m, $y equals 0$ . Calculate the magnitude and direction of the net electric field at the origin due to these two point charges.

Textbook Question

A point charge is placed at each corner of a square with side length $a$ . All charges have magnitude $q$ . Two of the charges are positive and two are negative (Fig. E $21.42$ ). What is the direction of the net electric field at the center of the square due to the four charges, and what is its magnitude in terms of $q$ and $a$ ?

Textbook Question

A $negative 4.00$ -nC point charge is at the origin, and a second $negative 5.00$ -nC point charge is on the $x$ -axis at $x equals 0.800$ m. Find the electric field (magnitude and direction) at each of the following points on the $x$ -axis: (i) $x equals 0.200$ m; (ii) $x equals 1.20$ m; (iii) $x = - 0.200$ m.

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Textbook Question

A charge of $negative 6.50$ nC is spread uniformly over the surface of one face of a nonconducting disk of radius $1.25$ cm. Why is the field in part (a) stronger than the field in part (b)? Why is the field in part (c) the strongest of the three fields? Note: Part (a) asked to find the magnitude and direction of the electric field this disk produces at a point $P$ on the axis of the disk a distance of $2.00$ cm from its center. Part (b) asked to find the magnitude and direction of the electric field at point $P$ , supposing that the charge were all pushed away from the center and distributed uniformly on the outer rim of the disk. Part (c) asked to find the magnitude and direction of the electric field at point $P$ if the charge is all brought to the center of the disk.

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 $x equals 0$ .