Question

5. (2 marks) A balance can be used to measure the strength of the magnetic field. Consider a loop of wire, carrying a precisely known current, shown in the figure, which is partially immersed (80 % of the total cross sectional area) in the magnetic field. The force that the magnetic field exerts on the loop can be measured with the balance, and this permits the calculation of the strength of the magnetic field. The short side of the loop measures 10.0 cm, the long sides are parallel and measure 15.0 cm each, the current in the wire is 0.225 A, and the resultant magnetic force is 5.35x 10 N What is the strength of the magnetic field?

Answer 1

AB = 10cm = .10m BC = 15cm = .15m CD = 10cm = .100m F = 5.35 times 10^- 2N I = 0.225 A and F = I(l^rightarrow times s^rightarrow) at every point l^rightarrow perpendicular to B^rightarrow F = IlB F_AB = I l_AB B F_BC = Il_BC B F_CD = Il_CD B F_AB = -F_CD F = F_BC F = Il_BC B B = F/Il_BC B = 5.35 times 10 ^- 2/0.225 times 0.15 B = 5.35/0.225 times 15 B = 1.58 T