Question

The rod in the slide-wire generator shown below is 40 cm in length and has a mass of 225 grams. The resistor is rated at 8 ohms. The rod is initially pulled to the right by some external agent.

deiegenerator shown below is 40 cm in length and has a mass of 225 grama. The resistor othe rght ly some ebnal ternal magvetic feld has strength of 1.5 Teslas. How much current passes through the resist Label the direction of this ournent in the dagam. neglected, what constant force muat be applied to knep the rod moving at this speed เชื7,take for 1 udf electruí energy to be converted tathermalemer bythe rustor? udling the rod to the right i uddenly token oway ot tine t the speed of the rod as function of tine, and derhve the equation that dcrbes the shap

a.) The uniform external magnetic field has strength of 1.5 Teslas. How much current passes through the resistor, if the speed of the rod is 20 m/s? Label the direction of this current in the diagram.

b.) if friction can be neglected, what constant force must be applied to keep the rod moving at this speed?

c.) how much time will it take for 1.0 kJ of electrical energy to be converted to thermal energy by the resistor?

The external force pulling the rod to the right is suddenly taken away at time t = 0.

d.) Sketch a graph of the speed of the rod as a function of time, and derive the equation that describes the shape of your graph.

e.) How much time will it take for the speed of the rod to drop from 20 m/s to 1 m/s?

Answer 1

a) induced emf = d phi/dt Emf = Blv Current = E/R = Blv/R = 1.5*0.4*20/8 = 1.5 amp b) Force required F = ilB = Blv*1*B/R = B^2 l^2 v/R = 1.5^2 times .4^2 times 20/8 = 0.9 N c) Power = i^2 R = 1.5^2 times 8 = 18 watt, now energy = power times time = 1000 j = 18 times t, then the time t = 1000/18 = 55.56 sec d) V_f = 20 e^-7.11 t is the relation.