The right resistor of the circuit from problem 3 is replaced with an open switch

Question

The right resistor of the circuit from problem 3 is replaced with an open switch as shown. Rank the magnitude of the potential difference across each component. If any are equal, state so explicitly. Explain. On the diagram, draw the charge distribution throughout the circuit. Will there be charges on the switch Explain why or why not. How does the magnitude of the electric field between the two ends of the switch compare to the magnitude of the electric field inside the resistor If either electric field is zero, stale so explicitly. Explain.

Explanation / Answer

Q3.

a. Potential difference across each of the three components, battery, resistor and open switch are equal. Since electrostatic field is conservative, net potential difference across a loop must be zero. As we go through a loop consisting of two of the above components, net potential difference is zero. So potential difference across each of them is equal.

b. There will be charges on the ends of battery, positive charge on higher potential end and negative charge on lower potential end. Small surafce charges are present on current carrying wires. No charges on open switch. Open switch is like a capacitor with small area of plates and a large distance between the plates. Hence capacitance is zero, even though there is potential difference between the plates, charge on the plates is negligible as capacitance is negligible.

c. magnitudes of both potential differences are equal. But magnitudes of both electric fields are not equal. Consider the expression V = Ed in a uniform field. Same V can be expressed as product of large field (E) and a small distance d or a small field E and a large distance d. First case is valid for a resistor and the second case for open switch.

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