Capacitance is the relationship between electric potential and the charge stored on conductors. The capacitance, C, is defined by q = CV where V is the potential difference between a pair of conductors, +q is the charge stored on one conductor, and -q is the charge stored on the other conductor. Here you will calculate the energy stored in a capacitor of capacitance C without regard to the shape of the conductors. They could be parallel plates, conducting spheres or oddly shaped lumps. a. If the potential difference between the two conductors is V, enter an expression for the change in the potential energy, U, when an infinitesimal amount of charge dq is moved from the conductor at a lower potential to the conductor at a higher potential. b. Create a new expression for the the change in the potential energy U by using the definition of capacitance to eliminate the potential V from the expression in the previous step. b. Assume that, initially, both conductors are uncharged and the potential energy of the system is zero. Infinitesimal amounts of charge are moved from the first conductor to the second until a total quantity of charge q has been transferred. Input an expression for the potential energy, U, of the system. Use only the variables provided which include q and C.
Capacitance is the relationship between electric potential and the charge stored on conductors. The capacitance, C, is defined by q = CV where V is the potential difference between a pair of conductors, +q is the charge stored on one conductor, and -q is the charge stored on the other conductor. Here you will calculate the energy stored in a capacitor of capacitance C without regard to the shape of the conductors. They could be parallel plates, conducting spheres or oddly shaped lumps.
a. If the potential difference between the two conductors is V, enter an expression for the change in the potential energy, U, when an infinitesimal amount of charge dq is moved from the conductor at a lower potential to the conductor at a higher potential.
b. Create a new expression for the the change in the potential energy U by using the definition of capacitance to eliminate the potential V from the expression in the previous step.
b. Assume that, initially, both conductors are uncharged and the potential energy of the system is zero. Infinitesimal amounts of charge are moved from the first conductor to the second until a total quantity of charge q has been transferred. Input an expression for the potential energy, U, of the system. Use only the variables provided which include q and C.
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