9. [20 pt=6+2+5+1+3+3] Consider a long infinite straight wire carrying a current $i$ as shown in Figure 9(a). Applying the law of
Biot-Savart, find the (a) manitude of the mangetic field at point P, a perpendicular distance R from the wire. [Hint:
$\int \frac{dx}{(x^2+a^2)^{3/2}} = \frac{x}{a^2(x^2+a^2)^{1/2}}$]
(b) Determine the direction (into the plane/out of the plane) of the magnetic field at P.
Consider an ideal solenoid which is infinitely long and consists of tightly packed turns of wire as shown in Figure 9(b). Let n be
the number of turns per unit length of the solenoid
(c) Applying Amper's law, find the mantidue of the magnetic field inside the solenoid carrying current $i$.
(d) Determined the direction of the magnetic filed inside the solenoid. (right or left along the solenoid axis)
A long solenoid with n number of turns per unit length and radius R carries a current of $i_s$, as shwon in Figure 9(c). A current of
$i_w$ exists in a straight conductor located along the central axis of the solenoid. (e) Find the radial distance from the axis at which
the dircetion of the magnetic field is 45° to the axial direction in terms of $i_s$, $i_w$ and n. (f) Is it possilbe to have 45° to the axial
direction if $i_w > 2\pi nR$? Explain.
