Force acting on a charge across a hybrid medium

  • #1
vcsharp2003
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Homework Statement
Two charge ##q_1## and ##q_2## are separated by two different dielectrics as shown in the diagram, having dielectric constants of ##K_1## and ##K_2##. The two charges are separated by a distance ##a##. What would be the force on charge ##q_2## due to charge ##q_1##?
Relevant Equations
##F = \dfrac {kq_1q_2} {Kr^2}##, where k is Coulomb's constant and K is dielectric constant, F is force of attraction between the two charges ##q_1## and ##q_2## that are separated by a distance ##r##

##E = \dfrac {kq} {Kr^2}##, where E is electric field due to a charge ##q## at a distance ##r## in medium having a dielectric constant ##K##
The force on charge ##q_2## will depend on the electric field in medium with dielectric ##K_2##.

Electric field in this second dielectric due to ##q_1## is ##E = \dfrac {kq_1} {K_2r^2}## where r would be the distance from ##q_1##.
So, the electric field at the point where charge ##q_2## is there would be ##E = \dfrac {kq_1} {K_2a^2}##

Therefore, force on second charge due to first charge would ##F_{21} = \dfrac {kq_1q_2} {K_2a^2} ##.
IMG_20211023_134338__01.jpg
 
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  • #2
Your answer would be correct if the entire distance ##a## had dielectric ##K_2##. The electric field at the boundary between dielectrics is ##\dfrac{kq_1}{K_1(\frac{3}{4}a)^2}##. What happens to it when you cross that boundary? In other words, what is continuous across the boundary?
 
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  • #3
kuruman said:
Your answer would be correct if the entire distance ##a## had dielectric ##K_2##. The electric field at the boundary between dielectrics is ##\dfrac{kq_1}{K_1(\frac{3}{4}a)^2}##. What happens to it when you cross that boundary? In other words, what is continuous across the boundary?
Thankyou for the answer.

My understanding is that the electric field in a medium becomes ##\dfrac {1} {K} ## times the electric field without any medium i.e. when there is vacuum, and I based my answer on this fact.

When the boundary of dielectrics is crossed from ##K_1## to ##K_2## then the electric field is still there except now it has a different formula i.e. a different strength, so electric field strength should not be a continuous function.
 
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