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Field Directions

Two equal, but opposite charges are placed on the [x] axis. The positive charge is placed at to the left of the origin and the negative charge is placed to the right, as shown in the figure above.

1)

What is the direction of the electric field at point [A]?

Right
- The opposite charges cancel along the [y] axis while [+Q] pushes along the positive [x] axis and [-Q] pulls allong the positive [x] axis.

2)

What is the direction of the electric field at point [B]?

Left
- Although the [+Q] charge is pushing to the right along the positive [x] axis at poiont [B], the [-Q] is pulling to the left along the negative [x] axis and hence the direction of the electric field at point [B] is leftward.

Magnitude of Field from Two Charges

In which of the two cases is the magnitude of the electric field at the point labeled [A] the largest?

The magnitudes are equal
- In both cases, the point is being acted on by forces in perpendicular directions. Case 1, the charge being pushed in along the positive [x] axis by [+Q] and pulled along the negative [y] axis by [-Q]. Case 2, the charge is being pushed along the postive [x] axis by the upper right [+Q] charge and pushed along the positive [y] axis by the bottom right [+Q] charge.

Motion of Test Charge

A positive test charge [q] is released from rest at distance [r] away from [a] charge of [+Q] and a distance [2r] away from a charge of [+2Q].

How will the test charge move immediately after being released?

To the right
- [ \frac{ Q}{ r^2} > \frac{ 2Q}{ 4r^2} = \frac{ Q}{ 2r} ]

Electric Fields

Two infinite lines of charge

Both lines have identical charge densities [+ \lambda \frac{ C}{ m}. Point [A] is equidistant from both lines and Point [B] is located above the top line as shown.

How does [E_A], the magnitude of the electric field at point [A], compare to [E_B], the magnitude of the electric field at point [B]?

[E_A < [E_B]
- Since all force along the [x] axis is zero in th field produced by infinite line of charge, both lines of chage have an identical charge density, and point [A] is equidiestant from both lines the magnitude of the force at point [A] is zero. The magnitude of the force at point [B] is greater than zero and therefore [E_A < [E_B].