E-Fields: Q&2Q Fixed on Y-Axis | Find Zero E-Field & Acceleration

[apphysicsgirl]

1. Homework Statement
Two charges, charge one is +Q and charge two +2Q, are fixed in a plane along the y-axis of an x-y coordinate plane. Charge one is at point (0,a) and Charge two is at the point (0,2a).
(a) Is there any portion of the y-axis in which the total electric field is zero? If so, where?
(b) If a small negative charge, -q, of mass m were placed at the origin, determine its initial acceleration (magnitude and direction).


2. Homework Equations

E1=E2
F=ma
E=F/q
E=1/4pi(epsilon not)xQ/r^2


3. The Attempt at a Solution

For (a), there will always be an e-field along the y-axis except for a point in between the two charges. I am having trouble finding that point, though. I set the two e-fields equal to each other, but was unsure of what to put as the radius for each.

For (b) I used F=ma and then plugged in F=Eq to get a=Eq/m. My final answer was (-1/4pi(epsilon not)x(Q/a^2+Q/2a^2)xq)/m.

 

[anathema]

I am also unsure of the direction of the acceleration, as it depends on the sign of the charges and the mass of the small negative charge.

Hello,

For part (a), you are correct that there will always be an electric field along the y-axis except at a point in between the two charges. To find this point, you can use the equation E1=E2, where E1 and E2 are the electric fields from charge one and charge two, respectively. The radius for each charge would be the distance from that charge to the point in between the two charges. In this case, it would be a for charge one and 2a for charge two. Solving for the point where the electric fields are equal will give you the point where the total electric field is zero.

For part (b), your approach is correct. To find the direction of the acceleration, you can use the fact that the direction of the electric field is always in the direction of the force on a positive charge. Since the small negative charge is placed at the origin, the direction of the electric field at that point will be towards the positive charges. Therefore, the direction of the acceleration will also be towards the positive charges.

 

[kerimek]

For (a), you are correct that there will be an electric field along the y-axis except for a point in between the two charges. This point is called the "neutral point" and can be found by setting the two electric fields equal to each other and solving for the distance from the origin. The radius for each electric field can be found using the distance formula, which is the distance between the point charge and the origin.

For (b), your approach is correct. The direction of the acceleration will be towards the positive charges, since the negative charge will be attracted to them. The magnitude of the acceleration can be found by plugging in the values for the electric field and the mass of the negative charge. Keep in mind that the electric field from both charges will contribute to the total acceleration.