# If there is enough charge getting moved by a magnetic field

#### michaelw

What happens?
For example, in the image at http://theory.uwinnipeg.ca/mod_tech/img145.gif the moving charge moving counterclockwise will induce a magnetic field out of the page. if there is enough charge moving , can it completely counter the magnetic field, and then move in a straight line? or am i misunderstanding something..

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#### OlderDan

Homework Helper
michaelw said:
What happens?
For example, in the image at http://theory.uwinnipeg.ca/mod_tech/img145.gif the moving charge moving counterclockwise will induce a magnetic field out of the page. if there is enough charge moving , can it completely counter the magnetic field, and then move in a straight line? or am i misunderstanding something..
Good question! The charges in the stream of charge in your diagram will indeed create their own magnetic field that will alter the field that was initially present in the region. You have the directions right. The net field will be weakened "inside" the arc of the charge and strengthened outside. Whether this will alter the path of the charges depends on what the net field is at the path of the charge. The fact that the charges add field on one side of the path and subract on the other side suggests that not much happens on the path itself.

Unfortunately, the mathematics for a loop of moving charge says that the field just inside the loop gets stonger as the loop is approached, and suddenly changes direction at the loop to be a stong field in the other direction. You might want to play around with this calculator to see what it suggests

http://www.netdenizen.com/emagnet/offaxis/iloopcalculator.htm

For easy comparison of the field components, start with a loop radius of a = 2*pi expressed to many decimal places and a current of 10,000,000. You will find that you cannot use x = 0 and r = a and get an answer, but you can approach those conditions and compare points just inside and just outside the loop, or points just barely to the left or barely to the right.

In reality, a beam of charge is not going to have only one exact radius. The added field should be smeared so that the change in field direction is gradual at the path of the charge. The "extra" field will be nearly zero at the loop radius. For less than a full circle things are of course more complicated, but a similar analysis should hold. The added field must change direction at the arc of the loop and should be about zero.

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