Electric field lines

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Question restatement: The topic is Electric field lines, and we must choose which statement about field lines is true among the options provided.
Option 1: 'leave negative charges and enter positive ones.' This is incorrect because electric field lines originate from positive charges and terminate on negative charges; they do not leave negative charges or enter positive ones. In a typical positive source, lines radiate outward, while from a negative sink, lines converge inward.
Option 2: 'are close together where E is weak and far apart where E is strong.' This is the opposite of the correct relationship. Field lines crowd together where the electric field is strong (high E) and spread out where E is weak (low E). Therefore this statement reverses the actual behavior.
Option 3: 'have the same pattern around a charged metal sphere as they do around a point charge.' This statement is true in the region outside a spherically symmetric charged metal sphere (a conductor) because the charge distributes uniformly on a conducting shell and, outside, the field is as if all the charge were concentrated at the center, producing radial, spherically symmetric field lines just like the field of a point charge. Gauss’s law and the symmetry of the setup support this analogy, so the pattern matches that of a point charge.
Option 4: 'physically exist.' This is a philosophical/metaphysical claim rather than a scientific one about the actual behavior of electric fields. Field lines are a convenient visualization used in physics, but they are not physical objects themselves; they are a mnemonic representation of the direction and relative strength of the field. Saying they physically exist mischaracterizes their nature, making this statement not true in the intended scientific sense.
In summary, the correct statement describes the equivalence in outside-field patterns between a charged metal sphere and a point charge, reflecting spherical symmetry and the inverse-square behavior of the field. The other options misstate the direction of line density with respect to field strength, invert the origin/termination of lines, or attribute physicality to the lines themselves. The reasoning aligns with standard electrostatics concepts such as field line behavior, conductor charge distribution, and the external field of a spherically symmetric charge distribution.

APPHYSC142-031 with labs Exam Review - Final

Electric field lines

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