\begin{problem*}{31.45}
A circular coil enclosing an area $A=0.0100\U{m$^2$}$ is made of $200$
turns of copper wire as shown in Figure~P31.45.  Initially, a uniform
magnetic field of magnitude $B=1.10\U{T}$ points upward in a direction
perpendicular to the plane of the coil.  The direction of the field
then reverses in a time interval $\Delta t$.  Determine how much
charge enters one end of the resistor during this time interval if
$R=5.00\U{Ohm}$.
\begin{center}
% B ^ ^ ^
%   | | |  (from back of coil)
%   +-+-+---+
%   +-+-+   Z R
%   +-+-+   Z
%   +-+-+---+
%   | | |  (from font of coil)
\begin{asy}
import Mechanics;
import ElectroMag;
import Circ;

real dx = 5mm;
real r = 5mm;
int n = 10;      // number of coil loops
real tense = 8;  // increasing tension flattens the coil loops

MultiTerminal R = resistor(dir=90, Label("$R$", align=E));
real rlen = R.terminal[1].y - R.terminal[0].y;
real xr = R.center.x - dx;
real xl = xr - 2*r;
real dy = rlen / n;
for (int i = 0; i < n; i += 1) {  // back sides of coil
  pair dout = S;
  if (i == n-1) {
    dout = E;
  }
  real y0 = R.terminal[0].y + i * dy;
  draw((xl, y0 + dy/2){N}..tension tense ..{dout}(xr, y0 + dy));
}
Vector B = BField(dir=90);
B.outline += linewidth(0.5mm);
vector_field(((xl+xr)/2, R.center.y+rlen/3), width=2*r, height=2*rlen, v=B);
for (int i = 0; i < n; i += 1) {  // front sides of coil
  pair din = S;
  if (i == 0) {
    din = W;
  }
  real y0 = R.terminal[0].y + i * dy;
  draw((xr, y0){din}..tension tense ..{N}(xl, y0 + dy/2));
}
draw((xr, R.terminal[0].y) -- R.terminal[0]);
draw((xr, R.terminal[1].y) -- R.terminal[1]);
\end{asy}
\end{center}
\end{problem*}

\begin{solution}
\end{solution}

