Boundary Conditions for Electrostatic Fields Boundary Conditions for

Boundary Conditions for Electrostatic Fields

Boundary Conditions for Electrostatic Fields • we need to decompose the electric field intensity E into two orthogonal components tangential component Et and orthogonal component En • For medium 1 and medium 2 we have;

Boundary Conditions for Electrostatic Fields

Boundary Conditions for Electrostatic Fields • Normal components

Boundary Conditions for Electrostatic Fields

Boundary Conditions for Electrostatic Fields • We have;

Boundary Conditions for Electrostatic Fields • Since ; • Dt is said to be discontinuous across the interface For a free of charge boundary; The normal component of E is discontinuous at the boundary

Boundary Conditions for Electrostatic Fields

Boundary conditions at a Dielectric/Conductor Interface -we already have Dielectric -inside a good conductor E=0 D=0 ET 1=0 Dn 1=ρs Conductor

Boundary conditions at a Dielectric/Conductor Interface • No electric field may exist within a conductor • The electric field E can be external to the conductor and normal to its surface

Boundary conditions at a Dielectric/Free Space Interface • Special case where εr is one • The boundary conditions are

Example: Two dielectric media with permittivity ε 1 and respectively ε 2 , are separated by a charge free boundary. The electric field intensity in medium 1 at point P 1 has a magnitude E 1 and makes an angle α 1. Determine the magnitude and direction of the electric field intensity at point P 2 in medium 2. P 1 α 2 α 1 P 2

The magnitude of E 2 :

More Practical Problems: Boundary Conditions For z ≤ 0, er 1 = 9. 0 and for z > 0, er 2 = 4. 0. If E 1 makes a 30 angle with a normal to the surface, what angle does E 2 make with a normal to the surface?

also Therefore and after routine math we find Using this formula we obtain for this problem q 2 = 14°.

Practical Problems: Electric Potential The potential field in a material with εr= 10. 2 is V = 12 xy 2 (V). Find E, P and D.