PRS08 Hollow Conductors O2 I2 O1 I1 A point charge +Q is placed at the center of the conductors. The induced charges are: 1. Q(I1) = Q(I2) = -Q; Q(O1) = Q(O2)= +Q 2. Q(I1) = Q(I2) = +Q; Q(O1) = Q(O2)= -Q 3. Q(I1) = -Q; Q(O1) = +Q Q(I2) = Q(O2)= 0 4. Q(I1) = -Q; Q(O2)= +Q Q(O1) = Q(I2)= 0 PRS08 Hollow Conductors (1) The inner faces are negative, the outer faces are positive. Looking in from each conductor, the total charge must be zero (this gives the inner surfaces as –Q). But the conductors must remain neutral (which makes the outer surfaces have induced charge +Q). PRS08 Hollow Conductors O2 I2 O1 I1 A point charge +Q is placed at the center of the conductors. The potential at O1 is: 1. Higher than at I1 2. Lower than at I1 3. The same as at I1 PRS08 Hollow Conductors (3) O1 and I1 are at the same potential O2 I2 O1 I1 A conductor is an equipotential surface. O1 and I1 are on the same conductor, hence at the same potential PRS08 Hollow Conductors O2 I2 O1 I1 A point charge +Q is placed at the center of the conductors. The potential at O2 is: 1. Higher than at I1 2. Lower than at I1 3. The same as at I1 PRS08 Hollow Conductors (2) O2 is lower than I1 O2 I2 O1 I1 As you move away from the positive point charge at the center, the potential decreases. PRS08 Hollow Conductors O2 I2 O1 I1 A point charge +Q is placed at the center of the conductors. If a wire is used to connect the two conductors, then positive charge will flow 1. From the inner to the outer conductor 2. From the outer to the inner conductor 3. Not at all PRS08 Hollow Conductors (1) Positive charge flows outward Positive charges always flow “downhill” – from high to low potential. Since the inner conductor is at a higher potential the charges will flow from the inner to the outer conductor. PRS08 Capacitor Circuit Three identical capacitors are connected to a battery as pictured. The battery is then disconnected. A How do the charge on A, B & C compare B C before and after the battery is removed? 1. 2. 3. 4. 5. 6. 7. BEFORE; QA = QB = QC; QA = QB = QC; QA = QB = QC; QA > QB = QC; QA > QB = QC; QA < QB = QC; QA < QB = QC; AFTER No Change QA > QB = QC QA < QB = QC No Change QA = QB = QC No Change QA = QB = QC PRS08 Capacitor Circuit 4. QA > QB = QC; No Change A B C The potential drop across A is the same as the sum of the potential drops across B & C. By symmetry VB=VC, so VA > VB=VC Since Q = CV, QA > QB = QC. When the battery is disconnected there is no reason for the potential to change or charge to flow so it doesn’t. PRS08 Dielectric in a Capacitor A parallel plate capacitor is charged to a total charge Q and the battery removed. A slab of material with dielectric constant κ is inserted between the plates. The charge stored in the capacitor 1. Increases 2. Decreases 3. Stays the Same PRS08 Dielectric in a Capacitor (3) The charge is unchanged Since the capacitor is disconnected from a battery there is no way for the amount of charge on it to change. PRS08 Dielectric in a Capacitor A parallel plate capacitor is charged to a total charge Q and the battery removed. A slab of material with dielectric constant κ is inserted between the plates. The energy stored in the capacitor 1. Increases 2. Decreases 3. Stays the Same PRS08 Dielectric in a Capacitor (2) The energy stored decreases The dielectric reduces the electric field and hence reduces the amount of energy stored in the field. PRS08 Dielectric in a Capacitor A parallel plate capacitor is charged to a total charge Q and the battery removed. A slab of material with dielectric constant κ is inserted between the plates. The force on the dielectric 1. pulls in the dielectric 2. pushes out the dielectric 3. is zero PRS08 Dielectric in a Capacitor (1) The dielectric is pulled into the capacitor We just saw that the energy is reduced by the introduction of a dielectric. Since systems want to reduce their energy, the dielectric will be sucked into the capacitor. Alternatively, since opposing charges are induced on the dielectric surfaces close to the plates, the attraction between these will lead to the attractive force.