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Chapter 22: Problem 13

Why do electric field lines never cross?

Short Answer

Expert verified
Answer: Electric field lines never cross because the electric field is unique at any point in space. Crossing field lines would imply that there is more than one value of electric field intensity at a given point, violating the fundamental laws of physics. This would lead to ambiguous conclusions about the direction and magnitude of the force acting on a charged particle at that location.

Step by step solution

01

Understanding the electric field

The electric field is a vector field, which means that at every point in space, there is an electric field vector associated with it. This vector represents the force experienced by a unit positive charge if it were placed at that point. That means the direction of the vector represents the direction of the force on the charge, and its magnitude represents the strength of the force.
02

Defining electric field lines

Electric field lines are a visual representation of how electric charge would influence the space around it. The lines are drawn so that the tangent to the line at any point represents the direction of the electric field at that point. The spacing of the lines is also significant; denser field lines indicate a stronger electric field, whereas sparser lines indicate a weaker field.
03

Explaining the uniqueness of electric field direction

The main reason electric field lines never cross is because of the uniqueness of the electric field direction at any point in space. If electric field lines were to cross, there would be two different electric field vectors (meaning two different directions) at that location. This would mean that a charged particle placed at the point of intersection would experience two different simultaneous forces, which is contradictory to the concept of electric field - the field acts with one unique force on the charge at that given point.
04

Visualizing the field lines of multiple charges

When we have more than one charge present, the total electric field at a point is the vector sum of the individual electric fields created by each charge. Although the individual field lines may appear to come close to each other, they essentially reshape themselves in response to the total electric field vector, ensuring that the lines never actually cross.
05

Understanding the consequences of crossing field lines

If electric field lines were to cross, it would imply that there is more than one value of electric field intensity at a given point in space, violating the fundamental laws of physics that state the electric field is unique at any point in space. This would lead to ambiguous conclusions about the direction and magnitude of the force acting on a charged particle at that location. In conclusion, electric field lines never cross because the electric field is unique at any point in space, and the lines serve as a visual representation of the direction and magnitude of the force on a charged particle at any given location.

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Most popular questions from this chapter

At which of the following locations is the electric field the strongest? a) a point \(1 \mathrm{~m}\) from a \(1 \mathrm{C}\) point charge b) a point \(1 \mathrm{~m}\) (perpendicular distance) from the center of a \(1-\mathrm{m}\) -long wire with \(1 \mathrm{C}\) of charge distributed on it c) a point \(1 \mathrm{~m}\) (perpendicular distance) from the center of a \(1-\mathrm{m}^{2}\) sheet of charge with \(1 \mathrm{C}\) of charge distributed on it d) a point \(1 \mathrm{~m}\) from the surface of a charged spherical shell of charge \(1 \mathrm{C}\) with a radius of \(1 \mathrm{~m}\) e) a point \(1 \mathrm{~m}\) from the surface of a charged spherical shell of charge \(1 \mathrm{C}\) with a radius of \(0.5 \mathrm{~m}\)

A body of mass \(M\), carrying charge \(Q\), falls from rest from a height \(h\) (above the ground) near the surface of the Earth, where the gravitational acceleration is \(g\) and there is an electric field with a constant component \(E\) in the vertical direction. a) Find an expression for the speed, \(v,\) of the body when it reaches the ground, in terms of \(M, Q, h, g,\) and \(E\). b) The expression from part (a) is not meaningful for certain values of \(M, g, Q,\) and \(E\). Explain what happens in such cases.

Two infinite sheets of charge are separated by \(10.0 \mathrm{~cm}\) as shown in the figure. Sheet 1 has a surface charge distribution of \(\sigma_{1}=3.00 \mu \mathrm{C} / \mathrm{m}^{2}\) and sheet 2 has a surface charge distribution of \(\sigma_{2}=-5.00 \mu \mathrm{C} / \mathrm{m}^{2}\). Find the total electric field (magnitude and direction) at each of the following locations: a) at point \(P, 6.00 \mathrm{~cm}\) to the left of sheet 1 b) at point \(P^{\prime} 6.00 \mathrm{~cm}\) to the right of sheet 1

Consider a hollow spherical conductor with total charge \(+5 e\). The outer and inner radii are \(a\) and \(b\), respectively. (a) Calculate the charge on the sphere's inner and outer surfaces if a charge of \(-3 e\) is placed at the center of the sphere. (b) What is the total net charge of the sphere?

Two parallel, uniformly charged, infinitely long wires carry opposite charges with a linear charge density \(\lambda=1.00 \mu \mathrm{C} / \mathrm{m}\) and are \(6.00 \mathrm{~cm}\) apart. What is the magnitude and direction of the electric field at a point midway between them and \(40.0 \mathrm{~cm}\) above the plane containing the two wires?
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