Question about point charges (electric field strengths)

[curiousjoe94]

Homework Statement

A +15μC point charge Q1 is at a distance of 20mm from a +10μC charge Q2. Explain why there is a point along the line between the two charges at which the electric field strength is zero. After this, calculate the distance from this point to Q1 and Q2.

The Attempt at a Solution

First of all, I know that both charges are the same, so their electric fields act in repelling each other. I'm going to guess that the reason why there's a point in which electric field strength is zero, is because at this point, both charge's respectively fields cancel each other out in equal measures, leaving a net field strength of zero.

Is more explanation okay?


On the second part of the question where I'm asked to calculate the distance of this point from Q1 and Q2, I'm really stuck. I know the equation for finding the electric field strength of a charge is:

E = Q/(4*pi*e*r^2)

where, E = electric field strength, e = epsilon nought, r = distance between the charge and P, Q = charge.

 

[Infinitum]

Hi curiousjoe! Welcome to PF

I'm going to guess that the reason why there's a point in which electric field strength is zero, is because at this point, both charge's respectively fields cancel each other out in equal measures, leaving a net field strength of zero.

Yep, that's correct

On the second part of the question where I'm asked to calculate the distance of this point from Q1 and Q2, I'm really stuck. I know the equation for finding the electric field strength of a charge is:

E = Q/(4*pi*e*r^2)

where, E = electric field strength, e = epsilon nought, r = distance between the charge and P, Q = charge.

Assume that the electric field is zero at a distance x from the 15μC charge. What is the field due to the 15μC there? and the 10μC? What should be the relation between them?

 

[Chestermiller]

On the second part of the question where I'm asked to calculate the distance of this point from Q1 and Q2, I'm really stuck. I know the equation for finding the electric field strength of a charge is:

E = Q/(4*pi*e*r^2)

where, E = electric field strength, e = epsilon nought, r = distance between the charge and P, Q = charge.

Remember that the E in your equations is only the magnitude of the field strength. The field strength is actually a vector quantity, and points in the direction from the test charge to the actual charge. So you have to add the field strength vectors from the two actual charges to get the total field strength vector.

Chet

 

[curiousjoe94]

Hi curiousjoe! Welcome to PF
Yep, that's correct
Assume that the electric field is zero at a distance x from the 15μC charge. What is the field due to the 15μC there? and the 10μC? What should be the relation between them?

Remember that the E in your equations is only the magnitude of the field strength. The field strength is actually a vector quantity, and points in the direction from the test charge to the actual charge. So you have to add the field strength vectors from the two actual charges to get the total field strength vector.

Chet

Right, here's what I get:

Field due to 15μC would be,

E = (15*10^-6)/(4*pi*e*x^2)

where x is the distance from 15μC charge and the point where net field strength is zeroField due to 10μC would be,

E = (10*10^-6)/(4*pi*e*y^2)

where y is the distance from the 10μC charge and the point where net field strength is zeo.Like chester said, I understand that I need to find the difference between (15*10^-6)/(4*pi*e*x^2) and (10*10^-6)/(4*pi*e*y^2) and then make it equal to zero (total resultant field strength), but that would still leave two unknowns, x and y. So I'm still unsure what to do.

 

[Infinitum]

Right, here's what I get:

Field due to 15μC would be,

E = (15*10^-6)/(4*pi*e*x^2)

where x is the distance from 15μC charge and the point where net field strength is zeroField due to 10μC would be,

E = (10*10^-6)/(4*pi*e*y^2)

where y is the distance from the 10μC charge and the point where net field strength is zeo.Like chester said, I understand that I need to find the difference between (15*10^-6)/(4*pi*e*x^2) and (10*10^-6)/(4*pi*e*y^2) and then make it equal to zero (total resultant field strength), but that would still leave two unknowns, x and y. So I'm still unsure what to do.

Yes, but what is y in terms of x?? The total distance between the charges is given! And a part is x...and the whole is the sum of its parts...

The field strength is actually a vector quantity, and points in the direction from the test charge to the actual charge.

It actually points away from the direction of the test charge to actual charge as both are positive

 

[curiousjoe94]

Yes, but what is y in terms of x?? The total distance between the charges is given! And a part is x...and the whole is the sum of its parts...

Oh of course!

x, and then 20 - x, I get it now

Thanks a lot!

 

[Infinitum]

Oh of course!

x, and then 20 - x, I get it now

Thanks a lot!

Good job!