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Problem 67 Easy Difficulty

A conducting rectangular loop of mass $M,$ resistance $R,$ and dimensions $w$ by $\ell$ falls from rest into a magnetic field $\overrightarrow{\mathbf{B}},$ as shown in Figure $\mathrm{P} 20.67$ . During the time interval before the top edge of the loop reaches the field, the loop approaches a terminal speed $v_{\mathrm{T}}$ (a) Show that
$$v_{T}=\frac{M g R}{B^{2} w^{2}}$$
(b) Why is $v_{T}$ proportional to $R ?$
(c) Why is it inversely proportional to $B^{2} ?$

Answer

a. v_{T}=\frac{M g R}{B^{2} w^{2}}
b. \text { See explanation for result. }
c. \text { See explanation for result. }

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Video Transcript

Hi, friends. This is a problem based on phenomena off electromagnetic induction. Here it is given a conducting law off mus m the distance our having that I mentioned with the w and length L is falling vertically through the uniformed magnetic field directed perpendicular to the plane of the loop. As soon the figure in the first part we have to show that it's a terminal velocity. Is we Omega Square, VT Upon Sorry. Okay. N g r. Upon we square omega in second part, we have to explain why turn military cities directly was not to register dates and inversely proportional to square off magnetic people. I had to see it. First part induced e m f is we eat amigo VT at terminal velocity at terminal velocity current flowing through it. Is he upon part and turn on Ed Velocity off the loop. Toby. Equal Tau terminal velocity Net force is zero. That is forced. Do toe. Magnetic field is equal in a project. Toe weight off the loop. So it will be ivy, amigo. It's called two mg. Substitute the value off current. You will get we Omega beauty upon our and Toby in tow. Omega is called toe energy. So terminal velocity you will get M g r Divided by square off magnetic field. En very total you. This is the quest part it Do you be part if the distance would be more? Yeah. Less current will flow. Yeah, smaller current will flow through the loop. Yeah, I want so Lupul attempt Lukeville Patail. Higher magnitude. So that magnetic force bill well is the angina Shepherd Magnetic forces proposal toe magnetic field? No. And current. While the current itself is personal toe feel Mhm has force will be directly was not toe we square and terminal velocity. It's inversely was not toe magnetic force. Hence it is inversely proportional to square off mag. Repeat, that's all. Thanks for watching.

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Top Physics 102 Electricity and Magnetism Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Farnaz M.

Other Schools

Physics 102 Electricity and Magnetism Bootcamp

Lectures

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