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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

A thin, flat washer is a disk with an outer diameter of \(10.0 \mathrm{~cm}\) and a hole in the center with a diameter of \(4.00 \mathrm{~cm} .\) The washer has a uniform charge distribution and a total charge of \(7.00 \mathrm{nC}\). What is the electric field on the axis of the washer at a distance of \(30.0 \mathrm{~cm}\) from the center of the washer?

A solid sphere of radius \(R\) has a nonuniform charge distribution \(\rho=A r^{2},\) where \(A\) is a constant. Determine the total charge, \(Q\), within the volume of the sphere.

A uniformly charged rod of length \(L\) with total charge \(Q\) lies along the \(y\) -axis, from \(y=0\) to \(y=L\). Find an expression for the electric field at the point \((d, 0)\) (that is, the point at \(x=d\) on the \(x\) -axis).

Four charges are placed in a three-dimensional space. The charges have magnitudes \(+3 q,-q,+2 q,\) and \(-7 q .\) If a Gaussian surface encloses all the charges, what will be the electric flux through that surface?

A solid nonconducting sphere has a volume charge distribution given by \(\rho(r)=(\beta / r) \sin (\pi r / 2 R) .\) Find the total charge contained in the spherical volume and the electric field in the regions \(rR\). Show that the two expressions for the electric field equal each other at \(r=R\).
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