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Chapter 21: Problem 1

Can electric field lines ever cross? Why or why not?

Short Answer

Expert verified
No, electric field lines cannot cross. This is because the electric field at any point is unique and if they crossed, that would imply two different directions of the electric field at that point of intersection, which is not possible.

Step by step solution

01

Understanding the properties of electric field lines

Electric field lines are diagrams that depict the strength and direction of the electric field surrounding a charged object. By definition, they have certain properties. One such property is that the lines start on positive charges and end on negative charges. They provide a pattern showing the direction that a positive test charge would be pushed if placed in the field. Essentially, they illustrate the vector field of the electric force.
02

Evaluating conditions for crossing lines

If electric field lines were to cross, then at the point of intersection, the field would have two directions which is not possible. Electric field at a point is unique and is the direction of the force experienced by a positive test charge placed at that point. So, the electric field lines cannot intersect each other.
03

Understanding the implications

From our understanding of the properties of electric field lines, having crossover field lines, which suggest that a test charge at the point of intersection of the lines would be subject to two electric field vectors simultaneously, is unfeasible. This would violate the property of uniqueness of the electric field at a point.

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Most popular questions from this chapter

Eight field lines emerge from a closed surface surrounding an isolated point charge. Would the number of field lines change if a second identical charge were brought to a point just outside the surface? If not, would anything change? Explain.

An electric field is given by \(\vec{E}=E_{0}(y / a) \hat{k},\) where \(E_{0}\) and \(a\) are constants. Find the flux through the square in the \(x-y\) plane bounded by the points \((0,0),(0, a),(a, a),(a, 0).\)

A flat surface with area \(0.14 \mathrm{m}^{2}\) lies in the \(x-y\) plane, in a uniform electric field \(\vec{E}=5.1 \hat{\imath}+2.1 \hat{\jmath}+3.5 \hat{k} \mathrm{kN} / \mathrm{C} .\) Find the flux through the surface.

A long, solid rod \(4.5 \mathrm{cm}\) in radius carries a uniform volume charge density. If the electric field strength at the surface of the rod (not near either end) is \(16 \mathrm{kN} / \mathrm{C},\) what's the volume charge density?

A solid sphere \(25 \mathrm{cm}\) in radius carries \(14 \mu \mathrm{C},\) distributed uniformly throughout its volume. Find the electric field strength (a) \(15 \mathrm{cm},\) (b) \(25 \mathrm{cm},\) and (c) \(50 \mathrm{cm}\) from its center.
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