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Charge $q_{1}=1.00 \mathrm{nC}$ is at $x_{1}=0$ and charge $q_{2}=3.00 \mathrm{nC}$ is

at $x_{2}=2.00 \mathrm{m}$ . At what point betwcen the two charges is the electric ficld cqual to zero?

0.732 $\mathrm{m}$

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Rutgers, The State University of New Jersey

Numerade Educator

University of Washington

Hope College

we have two point charges that are placed on the X axis. One is X is equal to X politics 10 So this porn charges one, then a cool up and other charges placed at X to physical to two meter. And this is a tree in in a cooler. All charges are positive. We consume over this direction is X axis. Um, we see ball charged a positive. So the direction off their forces from the three and a cool I'm in one little problem with the trolley. So the rector of these forces will cancel out somewhere here in the middle There will be a result in electric field will be zero. So we are asked to find eight distance. Let's say the distance from X one. Do at some point here recall this distance R D is the distance where the electric field of some off electric fields off with these board charged zero. Um, and we ride the equation for the electric field for charge. One gonna pull em and Trina Coolum dis distance. And so that will be. He went the boat when they like to feel both charged particles are equal, Then the uh, the distance at which the electric fields are equal will be, um the resultant will be a zero. So the electric field do took you one is a call to electric field. Do trick. You too. We could write electric Really took You wanted to distance d That is cake. You one divided by the square and we can write for ah three Nano Colin Charge, which we call it came to, um there will be k times que tu divided by to minus d distance where? So if from here to here is a D than the distance from here to here will be, uh, to minus t because the total distance from here to here is a two meter then, uh, our job is to simplify this expression for a D in Seoul. So after some syndication, we get here the quality equation that is a T square plus to do you minus two musical zero. We conform to simplify this equation and get the d to be, um, plus minus were ruled off a three minus one. We have a to one source here, so we'll pick Pick only the past. The one because we're looking for a distance between these two charges, she taken anything when this will be somewhere here, which we're not entrusted. So then our distance will be one point 73 two minus one. The distance at which the electric fields will be zero will be 0.732 meters.