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A single field line of a particular force field is shown to form a closed loop. Such a line can NEVER represent which of the following?

1. an electrostatic field
2. a magnetostatic field
3. a gravitational field of a mass at rest
4. an induced electric field

Correct answer: an electrostatic field

Solution

A closed field line means the line integral of the field around a loop is non-zero, which is impossible for a conservative field. Electrostatic fields are conservative, so their field lines start and end on charges and can never form closed loops. (Gravitational field lines are also non-closed, but among the options the standard intended answer for the closed-loop line is the electrostatic field.) Magnetic field lines are always closed, and induced (non-electrostatic) E-field lines form closed loops, so those are allowed.

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