2. gauss’s law · 2. gauss’s law formulas! flux from a uniform electric field: Φ e =eacosθ...

Study Union Physics II for Engineers

1. Electric Force and Electric Field

Formulas! ● Coulomb's Law: Fe = ke q1q2 r2/ ● Electric Field due to a point charge: E = keq r2/

● Electric Field due to charge distribution: E = ke ∫

r2dq

● Particle in an electric field: Fe = qE

Find the electric force on the 7µC particle

Find the electric field at point P produced by the uniformly charged rod given a=0.25m ℓ=4m and the total charge of the rod is Q=2C

2. Gauss’s Law Formulas!

● Flux from a uniform electric field: ΦE=EAcosθ

● Gauss’s law: ΦE= = A∮

E • d ε0

qinc

What is the net electric flux through the below cube? What is the net charge enclosed? (The electric field through each face is uniform and perpendicular to that face)

Charge shape and Gaussian surface

Line of charge: Point charge or sphere: Sheet of charge:

The magnitude of an electric field 0.025m away from an infinite line of charge was found to be 3 N/C. What is the charge density of the line of charge?

3. Electric Potential Formulas!

● Electric potential energy of two point charges: U= ke q1q2 r/ ● Electric potential (voltage) from a point charge: V=ke q/r ● Potential difference between two points (in an electric field): ΔV= -Ed ● Change in potential energy due to the movement of a point charge through an

electric field: ΔU=-q E∫b

as• d

● Electric potential from a continuous charge distribution V = ke ∫

r

dq

● Electric field is change in voltage per distance Ex=- dxdV

A particle with charge 2C moves 3m through a uniform electric field of magnitude 7N/C in the direction of the field. What is the change in electric potential (voltage) and electric potential energy?

What is the electric potential at point P?

4. Capacitance Formulas!

● Definition of capacitance: C= QΔV

● Energy stored in a charge capacitor: UE=Q2

2C ● Capacitance of a two plate capacitor: C= d

εA

A capacitor originally has a capacitance of 6µF. The distance between the plates is tripled and the area of the plates is cut in half. What is the new capacitance? What is the equivalent capacitance of the following circuit?

Rearrange the capacitors from the above circuit to maximize capacitance. What is the maximum capacitance?

5. Ohm’s law Formulas!

● Ohm’s Law: ΔV=IR ● Resistance of a uniform block of material:

R=ρ ℓa

● Power of a circuit element: P=IΔV

When 5.5V are applied to a cylindrical wire with radius 3.0mm and length 4.3m a current of 6A is observed. What is the resistivity of the material used in the wire?

6. Direct-current circuits

Formulas! ● Charge on a charging capacitor: q(t)=Qmax(1- e-t/RC) ● Charge on a discharging capacitor: q(t)=Qmax(e-t/RC)

Find the equivalent resistance of the circuit and the current through each resistor given that 35V are applied between a and b

Find I1 I2 and I3 using Kirchhoff’s rules

7. Magnetic Force and Magnetic Field Formulas!

● Force exerted on a straight wire in a magnetic field: FB=ILxB ● Force exerted on a bent wire in a magnetic field: dFB=IdsxB ● Torque on a current loop in a magnetic field: τ = IAxB ● Force on a charged particle moving through a magnetic field: FB=qvxB

● Definition of magnetic flux: ΦB= A∫

B • d

● Biot-Savart Law: dB= μ4π r2

Ids x r

Find the initial direct of deflection of each particle as it moves through the magnetic field

Find the magnitude and direction of the magnetic field at point P

8. Ampere’s law Formulas!

● Ampere’s Law: = μ0Is∮

B • d

● Magnetic field from a long straight wire: B = 2πrμ I0

Find the magnetic field at radius r given that r>R (the radius of the wire)

9. Faraday’s law Formulas!

● Faraday’s law of induction: ε = - d ΦB/dt

● Motional emf produced by a bar moving through a magnetic field: ε= Bℓv

10. Inductance Formulas!

● Self induced emf from an inductor: εL = -L di/dt ● Inductance of a coil: L= NΦB/i

● Current in an RL circuit when a battery is attached: i= (1-e-t/τ)εR

● Current in a RL circuit when a battery is removed: i= e-t/τεR

● Time constant in an RL circuit: τ = L/R

11. Alternating-Current Circuits

Formulas! ● Inductive reactance: XL=ωL

● Capacitive reactance:XC= 1ωC

● Impedance : Z= √R X )2 + ( L − X C2

● rms current: Irms=Imax/√2 =0.707Imax

● Average power: Pavg= I2rmsR= IrmsΔVcosø

12. Maxwell’s Equations and Electromagnetic Waves

Formulas!

● Displacement current: Id=ε0 dtdΦ E

● Pointing vector: S= E x B1μ 0

● Lorentz force law: F=qE+qv x B

Tips!

● If all else fails try conservation of energy ● Remember units ● V=IR !!! ● If you’re allowed to use a graphing calculator, use it

Equations and problems taken from: Serway, R. A., & Jewett, J. W. (2014). Physics for Scientists and engineers (9th ed.). Cengage Learning.