Calculating Forces in Electrostatic Fields w/ q & 4q

[bansal321]

Hello i have a problem that i need help with.

Two fixed charges 'q' and '4q' are positioned along an axis with a separation d=5cm

a) Calculate the forces acting on each charge

Attempt
- I understand that the the force eqn is F = qE
- I also understand that i need to work out the Electric field before i can calculate the force
- and the electric field eqn is E = (k*q)/r^2??

what i don't understand is what are the values for the charges? There is no specific value for them, but they are written as 'q' and '4q'

Can anyone please offer some clarity to this please.

Thank you

 

[Delphi51]

You haven't been given the value of q but it certainly matters - the higher the q, the stronger the forces. So you will have a "q" in your answers.

You can use E = (k*q)/r^2 and then F = QE or put it together and just use
F = k*q*Q/r².

 

[bansal321]

Thank you for the response!

ok so i understand now to use F = k*q*Q/r^2

for the charge 'q' i have => (9*10^9)*q*Q/25 => (3.6*10^8)*q*Q

would that be the final answer? Can i multiply q*Q to get Q^2? or should i just leave it as that?

 

[Delphi51]

Careful, you must convert your cm to meters. You don't want the two different Q's to appear in the final answer. Just put in "q" for one charge and "4q" for the other. You'll end up with a number times q².

The question actually asks for TWO forces, so you should really say something about the force on the q and the force on the 4q and how they are different.

 

[asteriatic]

for reaching out for help with your problem. I can provide you with some guidance on calculating forces in electrostatic fields with 'q' and '4q' charges.

First, let's define the values for 'q' and '4q'. These are variables that represent the magnitude of the charges. In other words, they can be any numerical value, but they must be consistent throughout the problem. For example, you could choose 'q' to represent 2 Coulombs and '4q' to represent 8 Coulombs. This means that '4q' is four times larger than 'q'.

Now, to calculate the forces acting on each charge, we need to use the formula for Coulomb's Law:

F = k * (q1 * q2) / r^2

where:
- F is the force between the two charges
- k is the Coulomb's constant, which has a value of 8.99 x 10^9 Nm^2/C^2
- q1 and q2 are the magnitudes of the two charges
- r is the distance between the two charges

In this case, we have two charges, 'q' and '4q', separated by a distance of 5 cm (or 0.05 m). So, the force between them would be:

F = (8.99 x 10^9 Nm^2/C^2) * [(q * 4q) / (0.05 m)^2]

= 1.798 x 10^-4 * q * 4q N

= 7.192 x 10^-4 * q^2 N

Since we have two charges, we need to calculate the forces acting on each one separately. For 'q', the force would be:

Fq = (7.192 x 10^-4) * (q^2) N

And for '4q', the force would be:

F4q = (7.192 x 10^-4) * (16q^2) N

So, the forces acting on 'q' and '4q' are dependent on the magnitude of the charges and are given by these equations.

I hope this helps to clarify the problem for you. Let me know if you have any further questions or need more assistance. Good luck with your calculations!