Which of the following statements about line integrals are true? (one or more than one maybe correct). Line integrals of conservative fields over closed loops are zero.Line integrals of conservative fields over closed loops are non-zero.If curl of the field is a zero vector, the field is non-conservative.Line integrals of conservative fields are path dependent.Line integrals of conservative fields are path independent.
Question
Which of the following statements about line integrals are true? (one or more than one maybe correct). Line integrals of conservative fields over closed loops are zero.Line integrals of conservative fields over closed loops are non-zero.If curl of the field is a zero vector, the field is non-conservative.Line integrals of conservative fields are path dependent.Line integrals of conservative fields are path independent.
Solution
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Line integrals of conservative fields over closed loops are zero: This statement is TRUE. By definition, a conservative vector field is one whose line integral over any closed loop is zero.
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Line integrals of conservative fields over closed loops are non-zero: This statement is FALSE. As mentioned above, the line integral of a conservative field over a closed loop is always zero.
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If curl of the field is a zero vector, the field is non-conservative: This statement is FALSE. In fact, it's the opposite. If the curl of a vector field is zero, the field is conservative, not non-conservative.
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Line integrals of conservative fields are path dependent: This statement is FALSE. The line integral of a conservative field is path independent. This means that the value of the integral only depends on the start and end points, not the specific path taken.
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Line integrals of conservative fields are path independent: This statement is TRUE. As mentioned above, the line integral of a conservative field is path independent.
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