Module 1: charge and fields

Part 1: Charge and Coulomb's force

• charged particles exert a force on one another proportional to the product of their charges.

• source of charge is proton and electron

• unis is Coulomb (C)

• charge is a quantized (integral multiples of some value)

  • minimum charge is that of the proton/electron: 1.6⋅10(-19)C

• charge = conserved

  • net charge of the universe is 0

Coulomb's force: (F_C)=k((q_1)*(q_2))/((r_12)2)*(r_12)

• k is a constant: k=1/(4*π*(ϵ_0))=8.99×109*N-m2/C2

• (r_12) is a unit vector equal to (r_12)/|(r_12)|

For multiple particles:

• forces add as vectors

• calculate force between each pair and sum to find totals

• superposition forces add independently of what other charges are there:

  (f_12)=(k*(q_1)*(q_2))/((r_12)2)*(r_12),(f_13)=(k*(q_1)*(q_3))/((r_13)2)*(r_13)

Example 1: particle 1 is at -2*i and charge 5*C, and particle 2 is at 1*i-3*j and charge -8 C

(r_12)=5

(F_C)=k|5*(-8)|/((r_12)2)*i=(40*k)/(52)=8/5*k*i=1.44⋅1010

Example 2: Consider the same particle from before, but add particle 3

given information: (q_3)=-2*C, x=4, y =4, and (q_2)=-8*C, x=3, y=0

(F_23)=k((q_1)*(q_2))/((r_23)2)*(r_23)

(r_23)=(r_3)-(r_2)=(4*i+4*j)-3*i=i+4*j

(r_23)2=1+16=17

(r_23)=(r_23)/√(,(r_23)2)=1/√(,17)*(i+4*j)