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Why can electric field lines never cross?

Short Answer

Expert verified

If the electric field lines cross at a location, the direction of the electric field at the same point is in the various direction that is impossible. That is why electric field lines never cross.

Step by step solution

01

Concepts

The electric field lines are an imaginary path for a test charge to move.

The direction of the electric field lines shows the direction of the electric field at any location.

02

Explanation

Let assume two electric field lines cross at a point. The two electric field lines have different directions, which means there are two different directions of the electric field at the same point. Having a different direction of the electric field at the same time is impossible. That is why the field lines never cross.

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Most popular questions from this chapter

The balloon in Fig. 16鈥48 was rubbed on a student鈥檚 hair. Explain why the water drip curves instead of falling vertically.

Consider the electric field at the three points indicated by the letters A, B, and C in Fig. 16鈥49. First draw an arrow at each point indicating the direction of the net force that a positive test charge would experience if placed at that point, then list the letters in order of decreasing field strength (strongest first). Explain.

(a) The electric field near the Earth鈥檚 surface has magnitude of about 150 N/C. What is the acceleration experienced by an electron near the surface of the Earth? (b) What about a proton? (c) Calculate the ratio of each acceleration to \({\bf{g = 9}}{\bf{.8}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\).

(II) A large electroscope is made with 鈥渓eaves鈥 that are 78-cm-long wires with tiny 21-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26掳 angle with the vertical (Fig. 16鈥55), what total charge Q must have been applied to the electroscope? Ignore the mass of the wires.

Question:Two point charges,\({Q_1} = - 6.7{\rm{ }}\mu {\bf{C}}\) and\({Q_2} = {\bf{1}}{\bf{.8 }}\mu {\bf{C}}\)are located between two oppositely charged parallel plates, as shown in Fig. 16鈥65. The two charges are separated by a distance of \(x = 0.47 m\). Assume that the electric field produced by the charged plates is uniform and equal to\(E = 53,000 N/C\). Calculate the net electrostatic force on\({Q_1}\) and give its direction.

FIGURE 16鈥65 Problem 55.

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