In the figure, a rectangular loop carrying current lies in the plane of a uniform magnetic field of magnitude $0.050 \mathrm{T}$. The loop consists of a single turn of flexible conducting wire that is wrapped around a flexible mount such that the dimensions of the rectangle can be changed. (The total length of the wire is not changed.) As edge length $x$ is varied from approximately zero to its maximum value of approximately $4.0 \mathrm{cm}$ the magnitude $\mathit{\text{τ}}$ of the torque on the loop changes. The maximum value of $\mathit{\text{τ}}$ is $4.80\times {10}^{-8}\mathrm{N} \mathrm{m}.$ What is the current in the loop?

 A positron with kinetic energy $950 \mathrm{eV}$ is projected into a uniform magnetic field $\overrightarrow{B}$ of magnitude $0.732 \mathrm{T}$, with its velocity vector making an angle of $89.0°$ with $\overrightarrow{B}$. Find (a) the period, (b) the pitch $p,$ and (c) the radius $r$ of its helical path. $\left(\sin 89°=0.99\right)$

Mass of a positron = $9.11\times {10}^{-31} \mathrm{kg}$

The figure shows a current loop $ABCDEFA$ carrying a current $i=3.00 \mathrm{A}$. The sides of the loop are parallel to the coordinate axes shown, with $AB=20.0 \mathrm{cm},$ $BC=30.0 \mathrm{cm},$ and $FA=10.0 \mathrm{cm}.$ In unit-vector notation, what is the magnetic dipole moment of this loop?

In figure, an electron accelerated from rest through potential difference $V_1=2.50 \mathrm{kV}$ enters the gap between two parallel plates having separation $d=16.0 \mathrm{mm}$ and potential difference $V_2=100 \mathrm{V}.$ The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. (a) In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? (b) If the potential difference is increased slightly, in what direction does the electron veer from straight-line motion.

Mass of electron = $9.1\times {10}^{-31} \mathrm{kg}$.

In the figure shown, a metal wire of mass $m=24.1 \mathrm{mg}$ can slide with negligible friction on two horizontal parallel rails separated by distance $d=2.56 \mathrm{cm}.$ The track lies in a vertical uniform magnetic field of magnitude $73.5 \mathrm{mT}$. At time $t=0,$ device $G$ is connected to the rails, producing a constant current $i=9.13 \mathrm{mA}$ in the wire and rails (even as the wire moves). At $t=61.1 \mathrm{ms},$ what is the wire's (a) speed and (b) direction of motion (left or right)?

At time $t_1,$ an electron is sent along the positive direction of an $x$ axis, through both an electric field $\overrightarrow{E}$ and a magnetic field $\overrightarrow{B},$ with $\overrightarrow{E}$ directed parallel to the $y$ axis. The figure gives the $y$ component $F_{\text{net},\mathrm{y}}$ of the net force on the electron due to the two fields, as a function of the electron's speed $v$ at time $t_1$. The scale of the velocity axis is set by $v_{\mathrm{s}}=200.0 \mathrm{m} {\mathrm{s}}^{-1}.$ The $x$ and $z$ components of the net force are zero at $t_1$. Assuming $B_{\mathrm{x}}=0,$ find (a) the magnitude $E$ and (b) $\overrightarrow{B}$ in unit-vector notation.