Question

Two particles with charges +2q and +q are separated by a distance r. The +2q particle has an electric field E at distance r and exerts a force F on the +q particle.
When the +q particle is replaced by a +3q particle, what will be the electric field and force from the +2q particle experienced by the +3q particle?

- E/3, 3F
- E, 3F
- E/3, F
- E,F

(b)

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Video Transcript

This is College Physics Answers with Shaun Dychko. Two particles are separated by a distance

*r*one particle has a charge of plus 2*q*and the other particle plus*q*and there's an electric field at this position due to the 2*q*charge and then the field is Coulomb's constant times this charge 2*q*divided by this distance*r squared*and this electric field is there regardless of whether or not there's a charge here which is to say that the electric field doesn't depend on this right-hand charge, it depends only on this left-hand charge. The force that this charge experiences I call it*F 1*because this is the first scenario— the before scenario—*F 1*is the second charge, which is positive*q*times the electric field strength. Okay! The after scenario comes when we replace the plus*q*charge with a plus 3*q*particle so what will the electric field and force be due to the plus 2*q*particle in this case? Well, the electric field will be unchanged because the electric field doesn't depend on what this charge is so it's still*k*2*q*over*r squared*. The force that this right-hand particle will experience however is going to be different now because its charge is plus 3*q*and so we have 3*q*multiplied by the electric field strength is the force on this second case and*q*times*E*is*F 1*so we make that substitution and then we can see that*F 2*is 3 times*F 1*and so the electric field is the same in the second scenario but the force is now 3 times what it was so the answer is (b).