(Solved): An infinitely long single wire with current I1 = 3.5 A and a rectangular wire loop with current I2 ...

An infinitely long single wire with current $I_l=3.5\mathrm{A}$ and a rectangular wire loop with current $I_2=0.25\mathrm{A}$ are in the same plane as shown. The dimensions of the loop are $a=0.038\mathrm{m}$ and $b=$ $0.185\mathrm{m}$. The infinite wire is parallel to side $\mathrm{AD}$ of the loop and at a distance $d=0.19\mathrm{m}$ from it. $13\%$ Part (a) Express the magnitude of the magnetic force $F_{ad}$, from $I_1$ on wire $\mathrm{AD}$ in terms of $I_1,I_2,d$ and the loop dimensions. $F_{ad}=\left({?}_0{\mathrm{I}}_1{\mathrm{I}}_2\mathrm{b}\right)/(2?\mathrm{d})?$ Correct! $13\%$ Part (b) Calculate the numerical value of $F_{ad}$ in N. $\begin{array}{l}{F}_{ad}=1.71?10^{(?7)}\\ F_{ad}=1.710\times 10^{?7}?\text{ Correct! }\end{array}$ $13\%$ Part (c) Express the magnitude of the magnetic force $F_{bc}$, from $I_1$ on wire BC in terms of $I_1,I_2,a,b$, and $d$. $F_{bc}=\left({?}_0{\mathrm{I}}_1{\mathrm{I}}_2\mathrm{b}\right)/(2?(\mathrm{a}+\mathrm{d}))?$ Correct! $13\%$ Part (d) Calculate the numerical value of $F_{bc}$ in N. $\begin{array}{l}{F}_{bc}=1.42?10^{(?7)}\\ F_{bc}=1.420\times 10^{?7}\end{array}$ $?$ Correct! $13\%$ Part (e) Is the force of $F_{ad}$ repulsive or attractive? Attractive. ? Correct! $13\%$ Part (f) Is the force of $F_{bc}$ repulsive or attractive? Repulsive. $?$ Correct! $13\%$ Part (g) The forces of $F_{ad}$ and $F_{bc}$ both act on the infinite wire $I_1$. Do they sum to produce a net attractive or repulsive force? Attractive. $?$ Correct! $13\%$ Part (h) Calculate the numerical value of the sum of the forces $F=F_{ad}?F_{bc}$ on the infinite wire in N. $13\%$ Part (a) Express the magnitude of the magnetic force $F_{ad}$, from $I_1$ on wire $\mathrm{AD}$ in terms of $I_1,I_2,d$ and the loop dimensions. $F_{ad}=\left({?}_0{\mathrm{I}}_1{\mathrm{I}}_2\mathrm{b}\right)/(2?\mathrm{d})?$ Correct! $13\%$ Part (b) Calculate the numerical value of $F_{ad}$ in $\mathrm{N}$. $\begin{array}{l}{F}_{ad}=1.71?10^{(?7)}\\ F_{ad}=1.710\times 10^{?7}?\text{ Correct! }\end{array}$ $13\%$ Part (c) Express the magnitude of the magnetic force $F_{bc}$, from $I_1$ on wire $\mathrm{BC}$ in terms of $I_1,I_2,a,b$, and $d$. $F_{bc}=\left({?}_0{\mathrm{I}}_1{\mathrm{I}}_2\mathrm{b}\right)/(2?(\mathrm{a}+\mathrm{d}))?\text{ Correct! }$ $13\%$ Part (d) Calculate the numerical value of $F_{bc}$ in $\mathrm{N}$. $\begin{array}{l}{F}_{bc}=1.42?10^{(?7)}\\ F_{bc}=1.420\times 10^{?7}?\text{ Correct! }\end{array}$ $13\%$ Part (e) Is the force of $F_{ad}$ repulsive or attractive? Attractive. $?$ Correct! $13\%$ Part (f) Is the force of $F_{bc}$ repulsive or attractive? Repulsive. $?$ Correct! $13\%$ Part (g) The forces of $F_{ad}$ and $F_{bc}$ both act on the infinite wire $I_1$. Do they sum to produce a net attractive or repulsive force? $?$ Correct!