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InterviewSolution
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A squareframe carryinga current I = 0.90 A is located in the same plane as a long straight wire carrrying a current I_0 = 5.0 A. The frome side has a length a = 8.0 cm. The axis of the frame passing through the mid-points of the opposite sides is parallel to the wire and is separated from it by the distance which is eta = 15 times greater than the side of the frame. Find : |
| Answer» <html><body><p></p>Solution :(a) Force of attraction between parallel currents <br/> `F_(1) = (mu_0)/(4pi) ( 2I I_0)/((2eta -1 )(a)/(2)` <br/> Similar force of repulsion between antiparallel currents <br/> `F_(2) = (mu_0)/(4pi) (4I I_0)/((2 eta + 1)a)` <br/> Net force of repulsion between the square frame and the long straight wire <br/> `<a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a> = F_1 - F_2 = (2 mu_0)/(pi a) (I I_0)/(2 eta^2 -1)` <br/> Putting values,`F = 0.05 mu N.` <br/> b) Work perfomed in turning the frame through `180^@` <br/> `W = int_0^(pi) tau d theta,` But `d tau = bar(dM) <a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a> bar (B)(r)` <br/> `dM = IdA - = 2a dr n B(r) = (mu_0)/(4 pi) (2I_0)/(r) n`. <br/> n = unit normal to the frame into the paper <br/> `therefore d tau = dM B sin theta` <br/> `theta` = angle between B(r) and dA during the rotation process. <br/> `thereforetau = int d tau (mu_0)/(4 pi). 2I I_(0) sin theta int_( eta a - a//2)^(eta a+a//2) (dr//r)` <br/> `= (mu_0)/(4pi) 2 I I_0a sin theta log_e (2eta + 1)/(2 eta-1) therefore` Workdone <br/> ` W = int_(0)^(pi) taud theta = (mu_0)/(4pi)2 I I_0 a <a href="https://interviewquestions.tuteehub.com/tag/log-543719" style="font-weight:bold;" target="_blank" title="Click to know more about LOG">LOG</a> ""(2eta +1)/(2 eta - 1) sin theta d theta` <br/> ` = (mu_0)/(pi) I I_0 a log ""(2 eta + 1)/(2 eta -1) = 0.1 <a href="https://interviewquestions.tuteehub.com/tag/44-316683" style="font-weight:bold;" target="_blank" title="Click to know more about 44">44</a> mu <a href="https://interviewquestions.tuteehub.com/tag/j-520843" style="font-weight:bold;" target="_blank" title="Click to know more about J">J</a>`</body></html> | |