Consider an ideal parallel-plate capacitor whose plates areinitially separated b
ID: 1679889 • Letter: C
Question
Consider an ideal parallel-plate capacitor whose plates areinitially separated by a distance d. Each of the capacitor plateshas surface area A. The capacitor has been fully charged by aconnection to a battery that provides a constant voltageV_bat. Note: All results below should be expressed only in terms of_0, A, d, and V_bat. a) Obtain an expression for U_i, the potential energy of thecapacitor when it is fully charged and the plates are separated bya distance d. b) The battery is then disconnected, and the plates are slowlypulled apart by means of an external agent until the plates areseparated by a distance 3d. Obtain an expression for U_f, thepotential energy of the capacitor when it is still fully chargedand the plates are separated by a distance 3d. c) The magnitude of the force of attraction F between theplates of such a capacitor can be evaluated from F = Q*E_one, whereQ and E_one denote (respectively) the magnitude of the charge onone plate and the electric field strength produced by the otherplate. Show that F = Q^2/(2*_0*A) d) Determine the work W done to separate the plates asdescribed above. For convenience, assume that only one plate ismove while the other plate is held fixed. As a result, W is thework done to move this one plate. e) Show that U_f - U_i = W, and explain why this resultmust holdtrue. Please provide step by step solutions... . Consider an ideal parallel-plate capacitor whose plates areinitially separated by a distance d. Each of the capacitor plateshas surface area A. The capacitor has been fully charged by aconnection to a battery that provides a constant voltageV_bat. Note: All results below should be expressed only in terms of_0, A, d, and V_bat. a) Obtain an expression for U_i, the potential energy of thecapacitor when it is fully charged and the plates are separated bya distance d. b) The battery is then disconnected, and the plates are slowlypulled apart by means of an external agent until the plates areseparated by a distance 3d. Obtain an expression for U_f, thepotential energy of the capacitor when it is still fully chargedand the plates are separated by a distance 3d. c) The magnitude of the force of attraction F between theplates of such a capacitor can be evaluated from F = Q*E_one, whereQ and E_one denote (respectively) the magnitude of the charge onone plate and the electric field strength produced by the otherplate. Show that F = Q^2/(2*_0*A) d) Determine the work W done to separate the plates asdescribed above. For convenience, assume that only one plate ismove while the other plate is held fixed. As a result, W is thework done to move this one plate. e) Show that U_f - U_i = W, and explain why this resultmust holdtrue. Please provide step by step solutions... .Explanation / Answer
Consider an ideal parallel-plate capacitor whose plates areinitially separated by a distance d. Each of the capacitor plateshas surface area A. The capacitor has been fully charged by aconnection to a battery that provides a constant voltageV_bat. Note: All results below should be expressed only in terms of_0, A, d, and V_bat. a) Obtain an expression for U_i, the potential energy of thecapacitor when it is fully charged and the plates are separated bya distance d.this is given by 0.5Cv*v where C isoA/d v is the
potential difference across the plates
b) The battery is then disconnected, and the plates are slowlypulled apart by means of an external agent until the plates areseparated by a distance 3d. Obtain an expression for U_f, thepotential energy of the capacitor when it is still fully chargedand the plates are separated by a distance 3d.
the charge on the capacitor remains constant and the energy isgiven by Q*Q/2C
C now becomes oA/3d Q=initialC*initial potential difference
=0A/d*v c) The magnitude of the force of attraction F between theplates of such a capacitor can be evaluated from F = Q*E_one, whereQ and E_one denote (respectively) the magnitude of the charge onone plate and the electric field strength produced by the otherplate. Show that F = Q^2/(2*_0*A)
THE CHARGE ON EACH PLATE IS A
where is the charge density hence=Q/A electric field due to the
other plate is /2o total is/o
so the force on each plate is Q*Q/2oA
d) Determine the work W done to separate the plates asdescribed above. For convenience, assume that only one plate ismove while the other plate is held fixed. As a result, W is thework done to move this one plate.
W=F*2d F Is as above and hence work done by the externalforce
e) Show that U_f - U_i = W, and explain why this resultmust holdtrue. this can be shown from the above results
and this has to hold because there is frictional or nonconservative forces
for the loss of energy hence the decrease in energy should equalthe work done
by the external force