$k=9\mathrm{.}00{10}^{9}Nm\frac{2}{C^2}$

$k^{\text{'}}=1\mathrm{.}00{10}^{-7}T\frac{m}{A}$

$e=1\mathrm{.}60{10}^{-19}C$

${}_o=4k^{\text{'}},m_e=9\mathrm{.}11**{10}^{-31}kg$

#$1.$ In the figure at the right, $C_1=7\mathrm{.}00f,C_2=15\mathrm{.}0f,C_3=1\mathrm{.}25f,$ and $V=24\mathrm{.}0$ volts.

a$)$ Find the equivalent capacitance connected to the battery.

b$)$ Find the charge on each capacitor, and the potential difference across each capacitor.

c$)$ Find the energy stored in each capacitor.

#$2.$

In the ngure above, a straight segment of wire $2\mathrm{.}00$ m long carries a current of $5\mathrm{.}00$ A to the left, as shown. The wire is in the presence of an external magnetic field of $6\mathrm{.}00$ T $.$

a$)$ Find the magnitude of the magnetic force on the wire.

b$)$ Find the direction of the magnetic force on the wire. Explain in detail.

#$3$ A cylindrical coil has $400$ turns and a radius of $3\mathrm{.}00$ cm $.$ The external magnetic field in the region of the coil is uniform and axial. The field rises from $6\mathrm{.}00{10}^{-2}T$ to $13\mathrm{.}0{10}^{-2}T$ in $1\mathrm{.}50$ minutes. Find the induced emf across the ends of the coil. The ends of the coil are attached to a resistor of $6$ ohms. Find the induced current I