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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

M=8(4.5−C) M=8(4.5-C) \newlineThe magnetic field, M M , in microtesla, at the center of a loop with a current of C C milliamps clockwise is given by the equation. By how many microteslas does the magnetic field change for a 11 milliamp increase in the current?\newlineChoose 11 answer:\newline(A) −8-8\newline(B) −4-4.55\newline(C) 2828\newline(D) 3636

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Q. M=8(4.5−C) M=8(4.5-C) \newlineThe magnetic field, M M , in microtesla, at the center of a loop with a current of C C milliamps clockwise is given by the equation. By how many microteslas does the magnetic field change for a 11 milliamp increase in the current?\newlineChoose 11 answer:\newline(A) −8-8\newline(B) −4-4.55\newline(C) 2828\newline(D) 3636
  1. Understand the equation: Understand the given equation.\newlineThe equation M=8(4.5−C)M = 8(4.5 - C) describes the magnetic field MM in microteslas as a function of the current CC in milliamps. We need to find out how much the magnetic field changes when the current increases by 11 milliamp.
  2. Calculate change in field: Calculate the change in the magnetic field for a 11 milliamp increase in current.\newlineLet's first calculate the magnetic field for a current CC. Then we will calculate the magnetic field for a current C+1C + 1 milliamp and find the difference between the two.
  3. Calculate field for C: Calculate the magnetic field for the current CC. Using the given equation, the magnetic field for current CC is M=8(4.5−C)M = 8(4.5 - C).
  4. Calculate field for C+1C+1: Calculate the magnetic field for the current C+1C + 1 milliamp.\newlineFor a current of C+1C + 1 milliamps, the magnetic field will be M′=8(4.5−(C+1))M' = 8(4.5 - (C + 1)).
  5. Simplify expression for M′M': Simplify the expression for M′M'.M′=8(4.5−C−1)=8(3.5−C)M' = 8(4.5 - C - 1) = 8(3.5 - C).
  6. Find change in field: Find the change in the magnetic field.\newlineThe change in the magnetic field ΔM\Delta M is the difference between M′M' and MM.\newlineΔM=M′−M=8(3.5−C)−8(4.5−C).\Delta M = M' - M = 8(3.5 - C) - 8(4.5 - C).
  7. Simplify expression for ΔM\Delta M: Simplify the expression for ΔM\Delta M. \newlineΔM=8(3.5−C)−8(4.5−C)=8×3.5−8C−8×4.5+8C\Delta M = 8(3.5 - C) - 8(4.5 - C) = 8 \times 3.5 - 8C - 8 \times 4.5 + 8C.
  8. Cancel out terms with C: Cancel out the terms with C.\newlineSince −8C-8C and +8C+8C are on opposite sides of the subtraction, they cancel each other out.\newlineΔM=8×3.5−8×4.5=28−36\Delta M = 8 \times 3.5 - 8 \times 4.5 = 28 - 36.
  9. Calculate final change: Calculate the final change in the magnetic field. \newlineΔM=28−36=−8\Delta M = 28 - 36 = -8 microteslas.

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