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Chapter 5: Problem 7

Make \(n\) the subject of the formula $$ J=\frac{n E}{n L+m} $$

Short Answer

Expert verified
Question: Given the formula $$\frac{nE}{nL + m} = J$$, find n in terms of E, L, J, and m. Answer: After making n the subject of the formula, we get: $$n = \frac{Jm}{E - JL}$$

Step by step solution

01

Clear the denominator

To clear the denominator, multiply both sides of the equation by \((nL + m)\): $$ J(nL + m) = \frac{nE}{nL + m}(nL + m) $$ This simplifies to: $$ J(nL + m) = nE $$
02

Distribute J

Distribute J to both terms within the parentheses: $$ JnL + Jm = nE $$
03

Isolate n terms

Move the \(JnL\) term to the right side of the equation to have all n terms on the right side: $$ Jm = nE - JnL $$
04

Factor out n

Factor n out on the right side of the equation: $$ Jm = n(E - JL) $$
05

Solve for n

Divide both sides of the equation by \((E - JL)\) to solve for n: $$ n = \frac{Jm}{E - JL} $$ Now, \(n\) is the subject of the formula.

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