Chapter 19: Q6CQ (page 694)
Discuss how potential difference and electric field strength are related. Give an example.
The electric field strength is a measure of potential gradient at any point in the field \(\Delta V = E \times d\)
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A bare helium nucleus has two positive charges and a mass of \(6.64 \times {10^{ - 27}}{\rm{ }}kg\) .
(a) Calculate its kinetic energy in joules at \(2.00\% \) of the speed of light.
(b) What is this in electron volts?
(c) What voltage would be needed to obtain this energy?
Suppose you have a \(9.00\;V\) battery, a \(2.00{\rm{ }}\mu F\) capacitor, and a \(7.40{\rm{ }}\mu F\)capacitor.
(a) Find the charge and energy stored if the capacitors are connected to the battery in series.
(b) Do the same for a parallel connection.
A battery-operated car utilizes a 12.0 V system. Find the charge the batteries must be able to move in order to accelerate the 750 kg car from rest to 25.0 m/s, make it climb a 2.00 x 102 m high hill, and then cause it to travel at a constant 25.0 m/s by exerting a 5.00 x 102 N force for an hour.
(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength for air\(\left( {3.0 \times {{10}^6}\;V/m} \right)\)/ if the plates are separated by\(2.00\;mm\)and a potential difference of\(5.0 \times {10^3}\;V\)is applied?
(b) How close together can the plates be with this applied voltage?
The voltage across a membrane forming a cell wall is \(80.0{\rm{ }}mV\) and the membrane is \(9.00{\rm{ }}nm\) thick. What is the electric field strength? (The value is surprisingly large, but correct. Membranes are discussed in Capacitors and Dielectrics and Nerve Conduction—Electrocardiograms.) You may assume a uniform electric field.
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