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Chapter 15: Problem 9

Can two electric field lines cross each other? Explain.

Short Answer

Expert verified
No, electric field lines cannot cross due to the unique direction of the electric field at any point.

Step by step solution

01

Understanding Electric Field Lines

Electric field lines are visual tools used to represent the electric field created by charges. They indicate the direction and strength of the field: lines emanate from positive charges and terminate at negative charges, with the field being stronger where the lines are closer together.
02

Concept of Crossing Lines

Consider what it would imply if two electric field lines were to cross at a point. At the point of crossing, there would be two different directions indicated for the electric field, which is a contradiction because the electric field at any given point must have a unique direction.
03

Implications of Field Direction

The electric field vector at any location is defined to have a specific magnitude and direction, meaning there cannot be two different field directions at a single point.
04

Conclusion: No Crossing

Since having two different electric field directions at the same point is impossible, it follows that electric field lines cannot cross each other.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electric Field Direction
Electric field direction is a crucial aspect of understanding electric fields. These directions are visually represented by electric field lines. Each line indicates the path that a positive test charge would follow under the influence of the field. The lines start on positive charges and end on negative charges. This is why the field lines move from a positive to a negative charge.
  • Uniqueness at Each Point: At any given point in space, the electric field direction is unique. It is defined by the tangent to the field line at that point.
  • No Crossing of Lines: If field lines were to cross, it would imply two different directions for the electric field at a single point, which is physically impossible.
Electric field direction helps in visualizing how forces act on charges in the field and supports the critical rule that electric fields do not overlap in different directions at the same point.
Electric Field Strength
Electric field strength is another core concept related to electric fields. It refers to the intensity of the field created by an electric charge, and it can affect how other charges within the field behave.
  • Measurement: The strength of the electric field (\( E \)) at a point is defined as the force (\( F \)) per unit charge (\( q \)) at that point, given by the formula \( E = \frac{F}{q} \).
  • Representation with Field Lines: The closer the field lines are to each other, the stronger the electric field in that region. Conversely, widely spaced lines indicate a weaker field.
Knowing the electric field strength helps predict how a specific charge will move within the field and the force it will experience. It gives a quantitative measure to the otherwise qualitative field line diagrams.
Electric Charges
Electric charges are fundamental to electric fields and determine the origin and direction of electric field lines. There are two types of electric charges: positive and negative. These charges interact with each other and their surroundings to create electric fields.
  • Like Repels, Opposites Attract: Charges of the same type repel each other, whereas opposite charges attract.
  • Source of Field Lines: Field lines begin at positive charges and end at negative charges. This creates a structured field that can be mapped by these lines.
Understanding electric charges is essential for seeing how forces operate within electric fields and how the direction and strength of these fields are determined. When examining any electrical phenomenon, comprehending charge dynamics and interactions is key.

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Most popular questions from this chapter

Suppose you bring a plastic rod near a plastic ball that is suspended by a thread. If the ball is repelled by the rod, what can you conclude about the net charge on the ball? Answer the same question if the ball is attracted to the rod.

A pair of parallel plates are charged with uniform charge densities of \(-35 \mathrm{pC} / \mathrm{m}^{2}\) and \(+35 \mathrm{pC} / \mathrm{m}^{2}\). The distance between the plates is \(2.3 \mathrm{~mm}\). If a free electron is released at rest from the negative plate, find (a) its speed when it reaches the positive plate and (b) the time it takes to travel across the 2.3-mm gap.

In a Millikan oil-drop experiment, using oil with a density of \(940 \mathrm{~kg} / \mathrm{m}^{3},\) a droplet with a charge of \(-3 e\) is just balanced against gravity in an electric field of \(11.5 \mathrm{kN} / \mathrm{C}\). (a) What is the direction of the electric field? (b) What is the size of the (spherical) droplet?

A point charge \(-1.2 \mu \mathrm{C}\) is \(0.50 \mathrm{~m}\) away from a second point charge \(+1.0 \mu \mathrm{C}\). The force on a third charge, \(+1.4 \mu \mathrm{C},\) placed exactly halfway between the other two is (a) \(0.44 \mathrm{~N}\), directed toward the negative charge; (b) \(0.11 \mathrm{~N}\), directed toward the negative charge; (c) \(1.76 \mathrm{~N}\), directed toward the negative charge (d) \(0.11 \mathrm{~N}\), directed toward the positive charge.

Three point charges are placed on the \(x\) -axis as follows: \(20 \mu \mathrm{C}\) at \(x=0 ; 30 \mu \mathrm{C}\) at \(x=0.50 \mathrm{~m} ;\) and \(-10 \mu \mathrm{C}\) at \(x=\) \(1.0 \mathrm{~m}\). Find the net force on each point charge.
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