In a dielectric with relative permittivity ε_r, what is the relation between E inside and E outside for a uniformly filled capacitor?

In a dielectric with relative permittivity ε_r, what is the relation between E inside and E outside for a uniformly filled capacitor?

• A. E_inside = ε_r E_outside
• B. E_inside = E_outside / ε_r
• C. E_inside = E_outside
• D. E_inside = E_outside × (ε0/ε_r)

Answer: (B)

A dielectric between the plates reduces the field inside because the material becomes polarized in response to the external field. The bound charges that appear oppose the applied field, lowering the effective field inside the dielectric. The key boundary idea is that, in the absence of free surface charge at the interface, the normal component of the displacement field D is continuous: D_out = D_in. In vacuum, D_out = ε0 E_out, while inside the dielectric D_in = ε0 ε_r E_in. Equating these gives ε0 E_out = ε0 ε_r E_in, so E_in = E_out / ε_r. So the electric field inside is smaller by a factor of ε_r compared to the field that would exist outside (in vacuum).

A dielectric between the plates reduces the field inside because the material becomes polarized in response to the external field. The bound charges that appear oppose the applied field, lowering the effective field inside the dielectric.

The key boundary idea is that, in the absence of free surface charge at the interface, the normal component of the displacement field D is continuous: D_out = D_in. In vacuum, D_out = ε0 E_out, while inside the dielectric D_in = ε0 ε_r E_in. Equating these gives ε0 E_out = ε0 ε_r E_in, so E_in = E_out / ε_r.

So the electric field inside is smaller by a factor of ε_r compared to the field that would exist outside (in vacuum).