Exam 1

Question 1

Derivation of Parallel Plate Capacitor Equation

Answer 1

• Electric Field is top + bottom
• Define surface charge density
• Sub SCD into E Field
• Uniform P.D = Ed

Question 2

Kirchhoff’s Junction Rule

Answer 2

The current entering a junction = The current leave the same junction

Question 3

Kirchhoff’s Loop Rule

Answer 3

The sum of voltages from sources of emf is equal to the voltage drops across components in a closed loop

Question 4

Derivation for magnetic field inside and outside of Solenoid

Answer 4

• No azimuthal field: Apply Ampere’s Law, but no current = no B field
• No radial field: Solve and apply solenoidal condition. B field from left and right cancel so B field radially = 0
• Z Field = Integrate rectangle outside, length l, r1, r2

Question 5

Solenoid Assumptions

Answer 5

• Long so can neglect end effects
• Numbers of turns is large, can assume axial symmtry
• Wire wound forward and back so no net current along axis

Question 6

Impedance of a resistor Derivation

Answer 6

• Voltage Source: V = V0 cos(wt)
• Ohms Law: I = V/R
• V and I are in phase
• Z = R

Question 7

Impedance of a capacitor Derivaiton

Answer 7

• Q = VC
• I = dQ/dt
• I = C dV/dt
• V = V0 cos(wt), so I =…
• V and I are out of phase
• I = C dV/dt (Complex notation)
• Ohms Law:, Z = 1/jwc

Question 8

Impedance of an Inductor derivation

Answer 8

• V = L dI/dt
• V = V0 cos(wt) so I=…
• V and I are out of phase
• V = L dI/dt with complex notation
• Ohms Law: Z = jwL

Question 9

Conditions for Step Up for Step Down Transformer

Answer 9

• Either N or ϵ
• Step Up : s > p
• Step Down : s < p

Question 10

Transformer emf and number of turns ratio

Answer 10

ϵs Np = ϵp Ns

Question 11

Transformer emf-current ratio and current-turns ratio

Answer 11

• No loss of power, so P=P
• ϵs Is = ϵp Ip
• Ns Is = Np Ip

Question 12

Gauss’s Law: Charged Sphere

Answer 12

• Gaussian Surface: Sphere, Charge Q and Radius a
• Volume charge density
• Symmetry: E and dS vectors
• Solve Gauss’s Law - In and Out of sphere

Question 13

Gauss’s Law: Line of Charge

Answer 13

• Gaussian Surface: Cylinder, Length L and Radius R
• Linear Charge Density
• Symmetry: E and dS vectors
• Solve Gauss’s Law - Left, Right and Curved

Question 14

Gauss’s Law: Plane of Charge

Answer 14

• Gaussian Surface: Cylinder, Area A
• Surface Charge Density
• Symmetry: E and dS vectors (z>0 and 0>z)
• Solve Gauss’s Law - Top, Bottom and Curved

Question 15

Capacitors in Series Derivation

Answer 15

• Same charge
• Different voltages
• V = V1 + V2
• V = Q/C

Question 16

Capacitors in Parallel Derivation

Answer 16

• Same voltages
• Different charges
• Q = Q1 + Q2
• Q = VC

Question 17

Ampere’s Law: Straight Wire

Answer 17

• Wire has Current = I
• BS Law: Bz = 0
• SC: Br = 0
• B = Bφ
• Circular Path along φ : dl = dl φ
• Solve Ampere’s Law

Question 18

Ampere’s Law: Cylindrical Conductor

Answer 18

• Cylinder has Current = I, Radius = a
• Current Density
• B field vector
• dl is circular path along φ
• Solve Amperes Law inside and Outside of cylinder