Question

7 Figure 3 (b) A conducting rectangular loop of wires whose sides are a and b (as in Figure 3) and electrical resistance R, enters in an area with a magnetic field B = B, yż. This magnetic field only exists in the area where x > 0 and Y > 0, as shown in Figure 3. The rectangular loop of wires slides without friction, with constant velocity v directed along the OX axis. Determine: (1) The magnetic force acting on each side of the rectangular loop as a function of X. (ii) The energy that will need to be provided to introduce the whole rectangular loop inside this area. Consider now that at instant t = 0 the rectangular loop was launched with an initial velocity V. If the equation of motion m dy dt =- B a*v 4R Determine the velocity whilst the rectangular loop is entering the area where B = Byż and the distance travel as a function of t and ve What will be the position of the loop for a zero induced current and magnetic force. (5)

Answer 1

we know, force acting on a wire A in a magnetic field is I I (di x die length of wire] B = magnetic field] so force on side Be and AD are - I (axB) = Bal singoo (%) – Bai ħ on the x direction Fore on side AB and De are I (RXB) = BI X Y Info quo 1 ") NA Energy from * required to introduce the loop to xt de into the loop is - = roda BIX da

get Now integrating to Energy from o to b we Bixdx al - BI62 11) indyBoat Boa 4R Pt 2 or (du s Botadt 0 V - I 4Rm. NO or Inva - B21 CV TARmz Beat So al [or, vevo e Rm D for BrBo loop B-Boa. 3 Ba? C B²a 7 Va e 4Rm. IS2 ARM z 22 - Bar lag orir da so se gemt at - Ba 4Rm & ARM az ott If mo fish current is induced then position would be not after t time with velocity vol.