(Solved): All questions please: Two infinite sheets of current flow parallel to the yz plane as shown. T ...

All questions please:

Two infinite sheets of current flow parallel to the $$y?z$$ plane as shown. The sheets are equally spaced from the origin by $$x_0=7.4\mathrm{cm}$$. Each sheet consists of an infinite array of wires with a density $$n=19$$ wires $$/\mathrm{cm}$$. Each wire in the left sheet carries a current $${\mathrm{I}}_1=3.5\mathrm{A}$$ in the negative $$z$$ direction. Each wire in the right sheet carries a current $${\mathrm{I}}_2=3\mathrm{A}$$ in the positive z-direction. 1) What is $$B_x(P)$$, the $$x$$-component of the magnetic field at point $$P$$, located at $$(x,y)=(?3.7\mathrm{cm},0)$$ ? 2) What is $$B_y(P)$$, the $$y$$-component of the magnetic field at point $$P$$, located at $$(x,y)=(?3.7\mathrm{cm},0)$$ ? 3) What is $$B_y(R)$$, the $$y$$-component of the magnetic field at point $$R$$, located at $$(x,y)=(?11.1\mathrm{cm},0)$$ ? 4) What is $$?\vec{B}?d\vec{l}$$ where the integral is taken around the dotted path shown, from a to $$b$$ to $$c$$ to $$d$$ to $$a$$. The path is a trapazoid with sides ab and $$cd$$ having length 13.1 cm, side ad having length $$7.9\mathrm{cm}$$, and side bchaving length $$12.7\mathrm{cm}$$. The height of the trapezoid is $$\mathrm{H}=12.9\mathrm{cm}$$. 5) What is $$B_y(S)$$, the $$y$$-component of the magnetic field at point $$S$$, located at $$(x,y)=(11.1\mathrm{cm},0)$$ ? 6) What is $${?}_a^b\vec{B}?d\vec{l}$$ where the integral is taken along the dotted line shown, from a to $$b$$.