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Formula Sheet – PHY 162 – Exam C Chapter 21: Electric Charge Coulomb’s Force Law: ⃗ ̂ Total electric force: ⃗ ⃗ ⃗ ⃗ ⃗ Electrostatic constant: Permittivity constant: Electric current: Charge quantization: ; where and the electron charge is – . Chapter 22: Electric Fields Definition: ⃗⃗ ⃗ , or ⃗ ⃗⃗ Electric field lines: At any point, ⃗⃗ is tangent to the line through that point. The magnitude of ⃗⃗ is proportional to the number of lines per unit area. Point charge (Coulomb’s Law): ⃗⃗ Total electric field at a point: ⃗⃗ Electric dipole moment: ⃗ along the z axis at ̂ ⃗⃗ ⃗ ⃗⃗ ⃗⃗ ̂ where two charges of charge ±q are placed . Electric dipole field Along the z axis (z»d): ⃗⃗ ̂ , in the +z direction. | | Along the x axis (x»d): ⃗⃗ ̂ , in the -z direction. | | Electric dipole in external field Torque: ⃗ ⃗ ⃗⃗ , Potential energy: ⃗ ⃗⃗ Chapter 23: Gauss’ Law Flux of electric field through surface: ∮ ⃗⃗ ⃗⃗⃗⃗⃗⃗ ⃗⃗ ∮ ⃗⃗⃗⃗⃗⃗ Flat surface and constant field: ∮ Constant field perpendicular to the surface: Gauss’ Law: ⁄ ∮ , or Charged isolated conductor: Cylindrical symmetry: ( ) Planar symmetry: ⃗ ⃗⃗ ⁄ ( ) ⁄( just outside, ) ⁄ Spherical symmetry: ( ) ( ) ⁄( ) inside Ch 24 Electric Potential Electric potential energy: forces. Electric potential: then . , where ( ) Uniform electric field: Since . Units: [ ] Electron-volt ( ): is the work done by all electric . If the potential is zero at infinity, ( ( , we have ) [ ] )( For an arbitrary electric field, we have is , and ) ∫ ⃗⃗ ⃗ and component form this is Point Charge: ⃗⃗ ⃗⃗ ⃗⃗. In . . For two or more charges, ∑ . Electric dipole: , where is the dipole moment, is the distance from the dipole center, and is measured from the dipole axis. Electric potential energy: Two charges have For a set of charges, ∑ Charged isolated conducting sphere of radius electric field at the surface is and charge : The Chapter 28: Magnetic Fields Magnetic field ⃗⃗ defined by the Lorentz force: ⃗ Units: [ ] ( ) ⃗ ⃗⃗, | | , (Tesla). Crossed fields: Particle passes if Uniform circular motion: . Magnetic force on a wire with current : ⃗ ⃗⃗ ⃗⃗ , Magnetic dipole moment of a current loop: Magnetic dipole in external field Potential energy: ⃗ ⃗⃗ ; Torque: ⃗ ⃗ ⃗⃗ . . Chapter 29: Magnetic Fields due to Currents 4 x 10-7 Tm/A Vacuum permeability constant: (Biot-Savart Law) Magnetic field generated by a current: ⃗⃗ Long straight wire: ( ) , Circular arc of wire: ∫ ⃗⃗, ( ( ) ⃗ ⃗ ) , attractive if in the same direction, repulsive if in opposite directions. Ampere’s Law: ∮ ⃗⃗ ⃗ . Long straight wire of radius : Outside ( ): ; ): ( ) . Ideal solenoid: , inside where ; Inside ( Ideal toroid: , inside; Magnetic field far along axis of a coil: . ). ( Force between two parallel currents: ⃗⃗ , outside. , outside. .