Solve =(0.10T)(2pi)(1.6*10^-3m)/(4pi*10^-7N*A^-2)

$$= \frac { ( 0.10 T ) ( 2 \pi ) ( 1.6 \times 10 ^ { - 3 } m ) } { ( 4 \pi \times 10 ^ { - 7 } N \cdot A ^ { - 2 } ) }$$

Evaluate

$$\frac{800TmA^{2}}{N}$$

Solution Steps

Cancel out 2\pi in both numerator and denominator.

$$\frac{0.1\times 1.6\times 10^{-3}Tm}{2\times 10^{-7}A^{-2}N}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{0.1\times 1.6\times 10^{4}Tm}{2A^{-2}N}$$

Multiply 0.1 and 1.6 to get 0.16.

$$\frac{0.16\times 10^{4}Tm}{2A^{-2}N}$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{0.16\times 10000Tm}{2A^{-2}N}$$

Multiply 0.16 and 10000 to get 1600.

$$\frac{1600Tm}{2A^{-2}N}$$

Cancel out 2 in both numerator and denominator.

$$\frac{800Tm}{A^{-2}N}$$

Differentiate w.r.t. A

$$\frac{1600ATm}{N}$$