Consider the equipotential diagram at the top of the next page showing two missh
ID: 1527525 • Letter: C
Question
Consider the equipotential diagram at the top of the next page showing two misshapen conductors (the shaded regions labeled I and II). One of the conductors has a net charge of +10 mu C and the other conductor has an equal and opposite charge of -10 mu C. e) Consider a positive charge placed at point P. Based on the equipotential diagram, will this charge naturally want to move to the left or to the right? Does the electric field point to the left or to the right? Based on your answer, which conductor, I or II, has the +10 mu C and which has the -10 mu C charge? Explain your answers. f) Sketch some electric field lines for this equipotential diagram. g) Estimate the strength of the electric field at point P. Assume that one 'box' of the graphing-paper grid corresponds to a length of d = 1 cm. h) This pair of conductors acts as a capacitor. What is the capacitance of this capacitor? i) How much work should it take to move a single electron (charge q = -e) from region I to region II? j) How much total energy is stored in this capacitor? k) Let region I be maintained at a voltage of -3 V. If the charge on each conductor were doubled, what would the new voltage of region II be?Explanation / Answer
At Since the electric field can be defined as minus the gradient of the electric potential, which means that electric field is opposite to the direction in which the potential increases.
[ ec{mathrm{E}}=- riangledown V]
we can notice that
For the conductor 1, the electric potential increases from the conductor to the outer equipotential surface. Then, the electric field of the conductor is like the electric field of a negative charge. Hence, we can conclude that this conductor has the charge of [mathrm{-10,mu C}]
For the conductor 2, the electric potential decreases from the conductor to the outer equipotential surface. Then, the electric field of the conductor is like the electric field of a positive charge. Hence, we can conclude that this conductor has the charge of [mathrm{+10,mu C}]
Since the conductor 1 is negatively charged and the conductor 2 is positively charged. the electric field between them is leftward (from the conductor 2 to the conductor 1)
so, a positive charge placed at the point P moves to the left