A small glass bead charged to +6.0 nC is in the plane that bisect...

Question

A small glass bead charged to +6.0 nC is in the plane that bisects a thin, uniformly charged, 10-cm-long glass rod and is 4.0 cm from the rod's center. The bead is repelled from the rod with a force of 840 μN . What is the total charge on the rod?

Accepted Answer

Hello, fellow physicists today, we're gonna 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, a tiny plastic spear charged with a net positive charge of plus 4.0 Nano Kums. It's located in the mid plain of a uniformly charged 8.0 centimeter long plastic rod and is 3.0 centimeters away from its center. A force of 650 micro newtons repels the spear from the rod, determine the rods accumulated charge. So that's our end goal is to find the rods accumulated charge. So we're given some multiple choice answers and they're all in the same units of nano columns. So let's read them off to see what our final answer might be. A is 27 B is 25 C is 35 and D is 20. OK. So first off, let us recall and use the equation for the electric force, let's call it equation one. So the electric force states that F is equal to the charge multiplied by the electric field. So with this relationship in mind. We can go on ahead and write that and we'll call it equation two. We can write that the force on a spear is equal to the charge of the spear multiplied by the electric field of the rod is equal to the charge of the sphere multiplied by S constant multiplied by the absolute value of capital Q divided by the radius of the orbit. Or I should rather say the distance between the spear and the center of the rod. In this case multiplied by the square root of R squared plus capital L divided by two all squared. OK. Where R, as we said is the distance between the sphere and the center of the rod and the capital L is the length of the rod. OK. So at this stage, it'd be helpful to write down all of our known variables. So let's know that Hulu's constant K is equal to 9.0 multiplied by 10 to the power of nine newtons multiplied by meters squared per Coolum squared. And the force acting on the sphere F is equal to 650 micro newtons which is equal to 650 multiplied by 10 to the power of six newtons and the charge acting on the sphere. So Q spear is equal to plus 4.0 nano columns, which is equal to 4.0 multiplied by 10 to the power of negative nine S. And the distance between the spear and the center of the rod R is equal to 3.0 centimeters which is equal to 0.03 m. And the length of the rod is equal to eight centimeters which is equal to 0.08 m. OK. So we can rewrite equation two to solve for the absolute value of capital Q which is the rods accumulated charge. So when we use a little bit of algebra to rewrite equation two to solve for the rods accumulated charge, we get that the absolute value of capital Q is equal to F divided by Q spear multiplied by Kums constant multiplied by R multiplied by the square root of R squared plus L divided by two squared. So now we could plug in our known variables and solve for the rods accumulated charge. So let's do that. The rods accumulate charge is equal to 650. So the force was 650 multiplied by 10 to the power of negative six newtons divided by the charge on the sphere which was 4.0 multiplied by 10 to the power of negative nine columns multiplied by Coolum is constant 9.0 multiplied by 10 to the power of nine newtons multiplied by meters squared per Coolum squared multiplied by R which was 0.03 meters multiplied by the square root of 0. meters squared plus L which was 0.08 m divided by two squared. OK. So when we plug that into a calculator, we'll find out that the rods accumulated charges 2.708 multiplied by 10 to the power of negative eight poms. Which when we multiply that by 10 to the power of nine, we can convert it to nano columns. So we'll get 27 nano columns, which is our final answer. So the absolute value of the charge accumulated on the rod is about 27 nano columns. Hooray, we did it. So that means our final answer has to be the letter A 27 nano columns. 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 small glass bead charged to +6.0 nC is in the plane that bisects a thin, uniformly charged, 10-cm-long glass rod and is 4.0 cm from the rod's center. The bead is repelled from the rod with a force of 840 μN . What is the total charge on the rod?

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