(Solved): 3a. A long wire has a current of \( 4 \mathrm{~A} \). The current flows straight for \( 1 \mathrm{ ...

3a. A long wire has a current of \( 4 \mathrm{~A} \). The current flows straight for \( 1 \mathrm{~m} \), turns \( 90^{\circ} \), flows another \( 1 \mathrm{~m} \), and returns to its starting point along a semi-circle. Calculate the magnetic field (direction and magnitude) at the center of the semi-circle. 3b. A set of two multiple-turn loops of wire have different currents and different flow directions, but same number of turns and same radius of \( 20 \mathrm{~cm} \). The left loop has a current of \( 5.0 \mathrm{~A} \). They are separated by \( R=20 \mathrm{~cm} \). The current flows counter-clockwise in the left loop and clockwise in the right loop (as viewed from the person to the right of the two loops). The magnetic field on the axis-of-symmetry \( 15 \mathrm{~cm} \) to the left of the left most loop is zero. What is the current in the right loop? \#4 current is set up through a truncated right circular cone of resistivity \( 731 \Omega \cdot \mathrm{m} \), left radius \( a=2.00 \mathrm{~mm} \), right radius \( b=2.30 \mathrm{~mm} \), and length \( L=1.94 \mathrm{~cm} \). Assume that the current density is uniform across any cross section taken perpendicular to the length. What is the resistance of the cone?