Why is it impossible for the lines of force of an electric field to cross one another?
like charges repel each other
a charged particle is deflected by an eletric field
like charges are arranged on the same line of force
a positively charged particle can travel in only one direction at any time
none of these is correct
Explanation
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The lines of force in an electric field represent the direction and intensity of the electric field at different points. Let’s explore why these lines cannot cross each other:
Nature of Electric Field Lines:
Electric field lines always start from positive charges and end on negative charges.
They never intersect because at any point, the electric field has a unique direction.
If they crossed, it would imply that the electric field at that point has two different directions, which is not possible.
Options Explained:
A. Like charges repel each other: This is true, but it doesn’t directly explain why electric field lines don’t cross.
B. A charged particle is deflected by an electric field: This is true, but it doesn’t address the specific question about field lines.
C. Like charges are arranged on the same line of force: This is incorrect. Electric field lines don’t necessarily follow the arrangement of charges.
D. A positively charged particle can travel in only one direction at any time: This is unrelated to the behavior of electric field lines.
E. None of these is correct: The correct answer.
Therefore, the correct answer is option E: “none of these is correct.” The behavior of electric field lines is a fundamental concept in electromagnetism.
The correct answer is:
A) like charges repel each other
Explanation:
If two lines of force were to cross, it would imply that at the point of intersection, the electric field has two different directions. However, according to the definition of an electric field, the direction of the field at any point is the direction of the force on a positive test charge.
Since like charges repel each other, the electric field lines emerge from positive charges and terminate on negative charges. If two lines were to cross, it would mean that a positive test charge would experience two different forces, which is not possible.
Therefore, electric field lines cannot cross each other.
