Electrostatics and magnetism

Coulomb’s law

Fe = kq1q2/r²

• K = 8.99 × 10^9 Nm²/c²

Electric Field formula

E = Fe/q = kQ/r²

Electric potential energy

U = kQq/r

• Electric potential = V = U/q

• V = kQ/r

Electric potential energy signs

Determined by the source charge which is either positive or negative

Voltage formula

Change in V = Vb - Va = Wab/q

• positive test charge will move from positive to negative

  • Decreases charge

• Negative test charge will move from negative to positive

  • Increases charge

In both cases, potential energy is decreasing

Special cases in electrostatics: electric dipoles

• V = kqd/r² cos theta

  • P = qd

    • P = dipole moment

  • therefore V = kp/r² cos theta

Special cases in electrostatics: perpendicular bisector

Electric potential at any point along the plane is 0

E field = ¼ pi e0 x p/r³

Special cases in electrostatics: net torque on dipole

T = pEsintheta

p = dipole

E = electric field

Diamagnetic material

No unpaired electrons/no magnetic field

Paramagnetic materials

Unpaired electrons; weakly magnetized in the presence of an external magnetic field

Ferromagnetic materials

Unpaired electrons and permanent atomic magnetic dipoles

• strongly magnetized in the presence of an external magnetic field

Long straight current carrying wire formula

B = u0 I / 2pi r

• R = perpendicular distance

• U0 = permeability of free space

Circular loop formula

B = u0 I / 2r

Right hand rule of circular current

Thumb points in the direction of the current; magnetic field = hand

Magnetic force formula

Fb = qvB sin theta

• charge must have perpendicular component of velocity

Magnetic force right hand rule

Thumb = direction of velocity vector

Fingers = direction of magnetic field lines

Palm = direction of force vector for positive

Back of hand = direction of force change for negative

Force on a current carrying wire formula

Fb = ILBsintheta

• current = flow of positive charge —> also use second right hand rule/current = thumb