Two equal positive charges are held fixed and separated by d

[Hamdi Allam]

Homework Statement

Two equal positive charges are held fixed and separated by distance D. Find the electric field vector along their perpendicular bisector. Then find the position relative to their center where the field is a maximum

There was another thread with this question but the suggestions/answer is unclear

The Attempt at a Solution

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From symmetry, should E along the i^ direction be 0 along the perpendicular bisector ?

and since the charges is the same, the E vector should be E = 2Kq/(y^2) j^. Am i correct for the first part of this question? Y is the distance along the perpendicular bisector relative to the center of the two charges.

I am stuck at the second part of this question

 

[Chestermiller]

You need to add the electric fields associated with each of the two charges vectorially. What is the y component of each of these fields (in terms of D and y)?

 

[Hamdi Allam]

You need to add the electric fields associated with each of the two charges vectorially. What is the y component of each of these fields (in terms of D and y)?

Hi,

Is this regarding the second portion of the question or the first?

 

[Chestermiller]

Hi,

Is this regarding the second portion of the question or the first?

Both.

 

[Hamdi Allam]

Both.

Would it be kq/y^2? I am not sure how D would be incorporated in the y component of the field

 

[Chestermiller]

Would it be kq/y^2? I am not sure how D would be incorporated in the y component of the field

What would be the magnitude of the force exerted by the charge at (-D/2,0) on a positive test charge q* located at (0,y)? What would be the x and y components of this force?

 

[Hamdi Allam]

What would be the magnitude of the force exerted by the charge at (-D/2,0) on a positive test charge q* located at (0,y)? What would be the x and y components of this force?

would the magnitude be: K*q*q/((d^2)/4 + y^2)
x component: K*q*q/((d^2/4)
y component: K*q*q/(y^2)

 

[Chestermiller]

would the magnitude be: K*q*q/((d^2)/4 + y^2)
x component: K*q/((d^2/4)
y component: K*q/(y^2)

The magnitude is correct, but the components are incorrect. You need to reconsider the trigonometry.

 

[Hamdi Allam]

The magnitude is correct, but the components are incorrect. You need to reconsider the trigonometry.

ohhhhhh, silly mistake

the x component would be: k*q*q*D/(2*((d^2)/4 + y^2)^3/2))
the y component would be: k*q*q*y/((d^2)/4 + y^2)^3/2)

Is this correct?

 

[Chestermiller]

ohhhhhh, silly mistake

the x component would be: k*q*q*D/(2*((d^2)/4 + y^2)^3/2))
the y component would be: k*q*q*y/((d^2)/4 + y^2)^3/2)

Is this correct?

yes