Electricity and Magnetism
# Magnetic Flux, Induction, and Ampere's Circuital Law

$3.2\text{ cm}$ and a straight line, as shown in the above figure, is lying in a uniform magnetic field $\vec{B}$ of magnitude $74\text{ mT}.$ The magnetic field is perpendicular to the straight line of the loop and makes an angle of $45^\circ$ with the plane of the semicircle. If the magnetic field is reduced to zero at a uniform rate during a time interval of $6.0\text{ ms},$ what is the approximate magnitude of the electromotive force induced in the loop during this interval?

A closed loop of wire that consists of a semicircle of radius$r=0.30\text{ m},$ as shown in the above figure. The loop lies in a uniform magnetic field $\vec{B}$ that is directed out of the screen. If the field magnitude is given by $B=4.0t^2+4.0t+3.0,$ where $B$ is in teslas and $t$ is in seconds, what is the approximate magnitude of the electromotive force induced around the loop by that field $\vec{B}$ at $t=5\text{ s}?$

Consider a conducting loop of a half-circle of radius$\vec{B}$ that is perpendicular to and directed into the screen, as shown in the above figure. The loop has width $W=3.0\text{ m}$ and height $H=2.0\text{ m}.$ If the magnitude of the magnetic field is given by $B=5t^2x^2,$ where $B$ is in teslas, $t$ is in seconds, and $x$ is in meters, what is the magnitude of the induced electromotive force around the loop at $t=0.30\text{ s}?$

A rectangular loop of wire is immersed in a nonuniform and varying magnetic field