M=8(4.5-C) The magnetic field, M, in microtesla, at the center of a loop with a current of C milliamps clockwise is given by the equation. By how many microteslas does the magnetic field change for a 1 milliamp increase in the current? Choose 1 answer: (A) -8 (B) -4.5 (C) 28 (D) 36

Question

M=8(4.5-C) The magnetic field,  M, in microtesla, at the center of a loop with a current of  C milliamps clockwise is given by the equation. By how many microteslas does the magnetic field change for a 1 milliamp increase in the current? Choose 1 answer: (A) -8 (B) -4.5 (C) 28 (D) 36

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Given Equation: We are given the equation M = 8(4.5 - C), where M is the magnetic field in microteslas and C is the current in milliamps. We need to find out how much M changes when C increases by 1 milliamp.Calculate M for C: Let's first calculate the magnetic field M for a current C. Then we will calculate the magnetic field M for a current C + 1. The difference between these two values will give us the change in the magnetic field for a 1 milliamp increase in the current.Calculate M for C + 1: For the current C, the magnetic field is M = 8(4.5 - C).Find Change in M: For the current C + 1, the magnetic field is M' = 8(4.5 - (C + 1)) = 8(4.5 - C - 1) = 8(3.5 - C).Simplify Expression: Now we find the change in the magnetic field, which is ΔM = M' - M. Substituting the expressions for M' and M, we get ΔM = 8(3.5 - C) - 8(4.5 - C).Calculate ΔM: Simplifying the expression for ΔM, we get ΔM = 8(3.5 - C) - 8(4.5 - C) = 8 * 3.5 - 8 * C - (8 * 4.5 - 8 * C).Notice that the -8 * C and +8 * C cancel each other out, so we are left with ΔM = 8 * 3.5 - 8 * 4.5.Calculating the values, we get ΔM = 28 - 36 = -8 microteslas.

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