1. The problem statement, all variables and given/known data A wire is bent into a square connected to the terminals of a 9 Volt battery. The wire is constructed of copper with diameter of 1 mm and is bent into a square with side length of 30 cm. If the battery has a mass of 50 g and internal resistance 0.1 Ω, what magnetic field (magnitude and direction) is needed in the shaded region to keep the system in equilibrium? The resistivity of copper is 1.7 x 10^(-8) Ω m with a density of 8920 kg/cubic meter. 2. Relevant equations B = (μI)/(2πL) Force in a wire = LI x B = LIB V = IR r = internal resistance = 0.1 Ω Resistivity ρ = (RA)/L d = 0.3 m 3. The attempt at a solution Well...I know that net force = 0 if the system is in equilibrium. The forces that I have identified are the weight and the magnetic force. Should I consider electric force as a possible force? Why do I even need the mass of the battery? Resistivity ρ = (RA/L) r = (ρL)/A = (1.7 x 10^(-8) Ω m)(0.3 m)/(π x 0.0005² m²) = 0.0065 Ω I = V/R = 9V/(0.1 Ω + 0.0065 Ω) = 84.5 A current flows clockwise from the positive terminal to the negative terminal. B = (μI)/(2πL) = [(4π x 10^-7 Tm/A)(84.5 A)]/(2π x 0.3 m) = 5.63 x 10^-5 T length L = 0.3 m μ = 4π x 10^-7 Tm/A Mass of the top part of the wire = (density)(volume) = (8920 kg/cubic meter)(π x 0.0005² m²)(0.3 m) = 0.0021 kg weight = mg = (0.0021 kg) Net force = magnetic force - weight = 0 LIB - mg = 0 LIB = mg B = (mg)/(LI) = (0.0021 kg x 9.8 m/s²)/(0.3 m x 84.5 A) = 8.12 x 10^-4 T In order to find the direction of the magnetic field, I tried using the right hand rule and found that the magnetic field points into the page. Does this seem to make any sense? I also think that the two parallel current carrying wires in the shaded region have currents in opposite directions so their forces should also cause them to repel. After solving it two different ways, I got two different answers of B = 8.12 x 10^-4 T and B = 5.63 x 10^-5 T. I'm also having trouble telling if the magnetic field points inward or outward; I think it points inward after using the right hand rule. Please help if you can. Thank you so much.