91影视

A uniform bar has mass 0.0120 kg and is 30.0 cm long. It pivots without friction about an axis perpendicular to the bar at point figure below. The gravitational force on the bar acts in the direction. The bar is in a uniform magnetic field that is directed into the page and has magnitude B = 0.150T . (a) What must be the current in the bar for the bar to be in rotational equilibrium when it is at an angle $\mathbf{u}\mathbf{=}\mathbf{30}\mathbf{掳}$above the horizontal? Use your result from Problem (A uniform bar of length carries a current in the direction from point to point . The bar is in a uniform magnetic field that is directed into the page. Consider the torque about an axis perpendicular to the bar at point that is due to the force that the magnetic field exerts on the bar. (a) Suppose that an infinitesimal section of the bar has length and is dx located a distance x from point . Calculate the torque about point due to the magnetic force on this infinitesimal section. (b) Use$\mathbf{蟿}\mathbf{=}{\mathbf{鈭�}}_{\mathbf{a}}^{\mathbf{b}}\mathbf{dt}$to calculate the total torque on the bar. (c) Show that is the same as though all of the magnetic force acted at the midpoint of the bar.) (b) For the bar to be in rotational equilibrium, should l be in the direction from a to b or b to a ?

Step by step solution

01

Definition of magnetic field

The term magnetic field may be defined as the area around the magnet behave like a magnet.

02

Determine the current and direction

The current can be calculated by the relation

$\begin{array}{r}\mathrm{I}=\frac{\mathrm{mgcos}\left(\mathrm{胃}\right)}{\mathrm{BL}}\\ \mathrm{I}=\frac{(0.0120\mathrm{kg})\left(9.80\mathrm{m}/{\mathrm{s}}^2\right)\cos 鈦�\left(30{.0}^{鈭�}\right)}{(0.150\mathrm{T})(0.300\mathrm{m})}\\ \mathrm{I}=2.26\mathrm{A}\end{array}$

Hence, The current I in the bar for the bar to be in rotational equilibrium when it is at an angle $\mathrm{u}=30掳$above the horizontal is I = 2.26A.

And the direction from the diagram is from a to b.

Hence, the direction from a to b.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!