A +2.0 nC charge is at the origin and a −4.0 nC charge is at x=1....

Question

A +2.0 nC charge is at the origin and a −4.0 nC charge is at x=1.0 cm.b. Would the net force be zero for an electron placed at the same position? Explain.

Accepted Answer

Hello, fellow physicists today, we're going to solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use. In order to solve this problem, we have three particles, one has a plus three nano Coolum charge located at the origin point. A another has a negative five nano Coolum charge at point B three centimeters away from the origin on the plus X axis. OK. So find the distance from the origin to a point between the two particles at which a particle with a negative one nano Coolum charge experiences zero net force. So that's our end goal is to find the distance from the origin to a point between the two particles at which a particle with a negative one nano colum charge experiences a zero net force. OK. So we're given some multiple choice answers here. Let's read them off to see what our final answer might be. A is X equals negative 1.03 centimeters. B is X equals 1.30 centimeters. C is X equals 3.00 centimeters. And D is there is no such place between the charges. OK. So since our goal is to find the distance of position X when a negative one nano Coolum charge particle experiences a zero net force between two particles, we need to start by solving this problem by calculating the magnitudes of the forces between the particle and each charge. So we need to recall the equation for Kums Law which states that the force is equal to Kums constant multiplied by the absolute value of charge one multiplied by charge two, all divided by R squared where R is the distance between the particles or the separation distance. OK. So considering the forces on particle one and two, let's call this equation one. So the force on particle one on P is equal to s constant multiplied by the charge of one or the absolute value of charge. One multiplied by the absolute value of charge two divided by R one multiplied by P squared which is equal to Kums constant multiplied by the absolute value of charge one multiplied by the absolute value of charge P divided by X squared. So now let's call this equation two. So focusing on the force on particle two. Now, so the force two on the particle, those of the force on particle two is equal to s constant multiplied by the absolute value of charge two multiplied by charge P or the absolute value of charge P I should say R two all divided by R two multiplied by P squared which is equal to Kums constant, multiplied by the absolute value of charge, one multiplied by the absolute value of charge, I should say charge two. So the absolute value of charge two multiplied by the absolute value of charge P divided by D minus X squared. OK. So now we can set equations one and two equal to each other and to solve for X. So let's do that. So K multiplied by the charge one absolute value of charge one multiplied by the absolute value of charge P divided by X squared is equal to Kums constant multiplied by charge two multi or the absolute value of charge two multiplied by the absolute value of charge P divided by D minus X square. So now we can plug in our known variables and note that K which is Kums constant and QP cancels out. So charge one is equal to three nano columns divided by X squared is equal to charge two which charge two is equal to negative five nano columns. But anything to the absolute power of a negative number gives us a positive number. So we'll get five nano columns divided by the distance which distance D so it was three centimeters. So it'd be three cm minus X because we do not know what X is square. OK. So now we can cross multiply and simplify which will give us three nano columns multiplied by three centimeters minus X squared is equal to five nano Coolum multiplied by X squared. OK. So now we can divide both sides by nano columns and then continue to simplify our f continue to simplify. And our final form should look like the following. It should be two X squared plus centimeters X minus 27 centimeters squared equals zero. So this should look really familiar. So this is the type of equation that we use in the, when it looks like this in this set up, we know we need to use the quadratic function. So let's quickly recall what the quadratic function is. So the quadratic function states that X is equal to minus B plus or minus square root B squared minus four ac all divided by two A. OK. So let's use the quadratic function, the sulfur X so X equals minus 18 centimeters plus or minus the square root of centimeters squared minus four, multiplied by two, multiplied by negative 27 centimeter squared all divided by two, multiplied by two. So that means when we plug this into a calculator for both the positive and the negative instances, we get X is equal to 1.3 centimeters and X is equal to negative 10. centimeters. OK. So since the negative charge between two particles would experience a net force towards the positive charge at any point X equals 1.3 centimeters is unacceptable. So there is no such place between the charges. So that is our final answer. So let's go back up to look at our multiple choice answers. So that means the correct answer has to be the letter D. There is no such place between the charges. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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A +2.0 nC charge is at the origin and a −4.0 nC charge is at x=1.0 cm.b. Would the net force be zero for an electron placed at the same position? Explain.

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