Chapter 30: Electromagnetic Induction

A $20\mathrm{cm}\times 20\mathrm{cm}$square loop has a resistance of $0.10\mathrm{\Omega }$. A CALC magnetic field perpendicular to the loop is $\mathrm{B}=4\mathrm{t}-2{\mathrm{t}}^2$, where $\mathrm{B}$is in Tesla and$\mathrm{t}$is in seconds. What is the current in the loop at $\mathrm{t}=0.0\mathrm{s},\mathrm{t}=1.0\mathrm{s}$,and$\mathrm{t}=2.0\mathrm{s}?$

A 100-turn, the 2.0-cm-diameter coil is at rest with its axis vertical. A uniform magnetic field $60°$away from vertical increases from $0.50\mathrm{T}$to $1.50\mathrm{T}$in $0.60\mathrm{s}$. What is the induced emf in the coil?

$A100$turn, $8.0cm$diameter coil is made of $0.50mm$diameter copper wire. A magnetic field is parallel to the axis of the coil. At what rate must $B$increase to induce a $2.0A$current in the coil?

What is the magnetic flux through the loop shown in FIGURE EX30.4?

Does the loop of wire in FIGURE have a clockwise current, a counterclockwise current, or no current under the following circumstances? Explain.

a. The magnetic field points out of the page and is increasing.

b. The magnetic field points out of the page and is constant.

c. The magnetic field points out of the page and is decreasing

A circular loop made from a flexible, conducting wire is shrinking. Its radius as a function of time is $r=r_0{e}^{-\beta t}$. The loop is perpendicular to a steady, uniform magnetic field $B$. Find an expression for the induced emf in the loop at time $t$.

A$10cm\times 10cm$square loop lies in the $xy$-plane. The magnetic field in this region of space is $B=\left(0.30t\widehat{ı}+0.50t^2\widehat{k}\right)\mathrm{T}$, where $t$is in $s$. What is the $emf$induced in the loop at $\left(a\right)t=0.5s$and $\left(b\right)t=1.0s.$

A spherical balloon with a volume of $2.5\mathrm{L}$is in a $45\mathrm{mT}$uniform, vertical magnetic field. A horizontal elastic but conducting wire with $2.5\Omega$resistance circles the balloon at its equator. Suddenly the balloon starts expanding at $0.75\mathrm{L}/\mathrm{s}$. What is the current in the wire $2.0\mathrm{s}$later?

A $3.0-cm$-diameter, $10$-turn coil of wire, located at $z=0$in the$xy$-plane, carries a current of $2.5A.A2.0-mm$-diameter conducting loop with $2.0*10-4\Omega$resistance is also in the $xy$plane at the center of the coil. At $t=0s$, the loop begins to move along the $z$-axis with a constant speed of $75m/s$. What is the induced current in the conducting loop at$t=200ms?$The diameter of the conducting loop is much smaller than that of the coil, so you can assume that the magnetic field through the loop is everywhere the on-axis field of the coil.

A $20$cm$*20$cm square loop of wire lies in the $xy$-plane with its bottom edge on the $x$-axis. The resistance of the loop is$0.50\Omega$. A magnetic field parallel to the $z$-axis is given by$B=0.80y2t$, where$B$ is in tesla, $y$in meters, and$t$ in seconds. What is the size of the induced current in the loop at $t=0.50s$?