Magnetic Force In this lab, we observed the force that a magnetic field exerts on a current-carrying wire. Once we determined this force, we were able to determine the strength of the applied magnetic field. In this lab, we had two parts and each part had its own mass (20g and 10g) to achieve different results and trials. We used the FB=ILB equation in order to get magnetic force. Theory: Derivation of 3 Exact Result: To derive the equation d= LwB 4mg I , we first start with F b − F tx − F ty = 0. We know that Ft=mg, so we get F b = 4F td/L , which would end up becoming 4mgd/L. We also have F b = I BW , once we combine both equations we get 4mgd/L = I BW . Lastly, once we completely derive it we get the equation d= LwB I 4mg . Simplifying in Appropriate Limit: In this case, equation 3, d= LwB 4mg I , d is the only small enough value so the length of its diagonal can be << L/2. If d was greater, the diagonal length would also increase, thus d has to be less than L/2. Calculations: Shown on Excel Sheet. Results: (Comparing Magnetic Field Strength) The strength of the earth’s magnetic field is 10^-5 T, our magnetic field was just 0.411 T, is very surprising because the earth is huge however its magnetic field is just 10^-5T more than the magnetic field in this lab. The magnets used in MRI can vary some are 0.5 T and some are 3 T. Error Analysis: (Small Angle Approximation) If we were to compute the maximum angle θ, we would get 1.5 degrees. The small angle approximation would be measured in radians. So we would get θ=1.5*2*π/360 and we would get approximately 0.25 which is not far off from the true value of sine. The actual d value based on the exact formula for d is larger than the small angle approximation value. Conclusion: Overall, we were pretty satisfied with our lab results as our B measurement in part 2, which was 0.379397965+/-0.0008700994223 T agrees with the first mass 0.4113343465+/-0.4113343465 T within the uncertainty. It was a fairly simple lab that we performed and luckily we did get great values. The only possible error that could have happened was systematic error where it reads the magnetic force incorrectly, but it was correct throughout our whole experiment.