1.) A very long solenoid with a circular cross section and radius r1= 2.80 centimeters with ns= 290 turns/cm lies inside a short coil of radius r2= 3.50 centimeters and Nc= 43 turns. If the current in the solenoid is ramped up from zero at a constant rate from zero to Is= 2.30 Amperes over a time interval of 50.0 milliseconds, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing? Note that the magnetic field of a solenoid is given by B = µ0 n I where n is the number of turns per unit length. 2.) vertical magnetic field decreases at a rate of 94.0 mT/s. A flat circular coil of 780 turns with a 25.0 cm diameter has a 64 uF capacitor across its terminals. If the coil is placed perpendicular to the field, what is the charge on the capacitor? 3.) A motor has an armature resistance of 4.87 Ohm. If the motor draws 6.15 A when running at full speed and connected to a 120 V supply line, how large is the back EMF? What would the current in the motor be if the load causes it to run at half speed? Assume that the supply voltage is fixed