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$\bullet$$\bullet \mathrm{A}-5.00 \mathrm{nC}$ point charge is on the $x$ axisat $x=1.20 \mathrm{m} . \mathrm{A}$ second point charge $Q$ ison the $x$ axis at $-0.600 \mathrm{m} .$ What must be thesign and magnitude of $Q$ for the resultant electric field at theorigin to be (a) 45.0 $\mathrm{N} / \mathrm{C}$ in the $+x$ direction, $(\mathrm{b}) 45.0 \mathrm{N} / \mathrm{C}$ inthe $-x$ direction?

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a) $5.5248 \times 10^{-10} \mathrm{C}$b) $-3.052 \times 10^{-9} \mathrm{C}$

Physics 102 Electricity and Magnetism

Chapter 17

Electric Charge and Electric Field

Gauss's Law

Electric Potential

University of Washington

Hope College

University of Sheffield

University of Winnipeg

Lectures

13:02

In physics, potential energy is the energy possessed by a body or a system due to its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units (SI) is the joule (J). One joule is the energy expended (or work done) in applying a force of one newton through a distance of one metre (1 newton metre). The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concepts of potentiality. Potential energy is associated with forces that act on a body in a way that the work done by these forces on the body depends only on the initial and final positions of the body, and not on the specific path between them. These forces, that are called potential forces, can be represented at every point in space by vectors expressed as gradients of a scalar function called potential. Potential energy is the energy of an object. It is the energy by virtue of a position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force that works against the force field of the potential. This work is stored in the field, which is said to be stored as potential energy.

18:38

In physics, electric flux is a measure of the quantity of electric charge passing through a surface. It is used in the study of electromagnetic radiation. The SI unit of electric flux is the weber (symbol: Wb). The electric flux through a surface is calculated by dividing the electric charge passing through the surface by the area of the surface, and multiplying by the permittivity of free space (the permittivity of vacuum is used in the case of a vacuum). The electric flux through a closed surface is zero, by Gauss's law.

06:19

$\mathrm{A}-5.00$ -nC poin…

05:14

A $-$3.00-nC point charge …

03:39

A -3.00 nC point charge is…

02:18

08:43

$A+2.00-n C \quad$ point c…

12:16

A negative point charge $q…

16:24

A $+$2.00-nC point charge …

16:28

A +2.00 nC point charge is…

08:49

A point charge of $-4.00 …

06:10

$\bullet$$\bullet$ A point…

02:13

Point charge $q_{1}=-5.00 …

in this problem. We're going to use this formula for the electric field in terms of the charge and the distance between the point and the charge. We have to remember that the electric field points towards the negative charges and on the way from the positive charge. So if we have a reference point P here, we know there's a charge of negative five Nano columns over to the right and because he points towards the negative charges, there's going to be an electric field one due to that charge. And overall, we want the electric field at point B to be pointing this way with magnitude. It was like 45 Nana Cool. So we want he acts to be 45 Nana are nudes for cool. Sorry Newtons for cool to the right until his first apply this formula to find even one and so he want is equal to K, which is a constant times. The charge Q, which is minus five Nana cools so five times tends to my sign over the distance square. This distance here is given in the problem as 1.2 meters, some 1.2 square. This gives an evil in value of 31 point to Newman's for cool, and it's in a positive direction. If this is the positive extraction here now because we want an ultimate field of 45 what we have to do is take E x is equal to anyone. Plus, he too. Orry too is Thie electric field. Due to this charge capital Q solving for E too is e X minus one and we know what yes must be. It must be positive. 45 Anyone we just found to be positive 31. So this yields e t is equal to positive 13.8 noons for cooling. So hee to must also be pointing this way, right? That's me too. And if he too is pointing this way, that means that queue here must be positive sense. Electric field points away from a positive charges. So let's figure out what its magnitude is. We know he too must be this. So what is the magnitude of the charge? Well, E too is equal to K as a man. You to thank you over our square and then this gets cue is equal to eat too. Our square over. Okay, and then playing it. Everything we know now we get that the acid Valium Q must be 5.53 times 10 to the mice. 10 now should they remind us on there? Well, we determined that he, too, is positive. And the capital Q. Here is a positive charge, and so there should be a positive sign there. So that's what you must be now on to Barbie. It's the same style problem. Except now we're told that E X is equal to negative 45 not positive for five Nance for cool. And so hee, too, which is still evil. Teo X minus. The one is now equal to negative 76.2 noons per cool. And so now we do the same thing here, except we plug in this for you too. And another thing we need to know is that since he too is negative, it's now pointing this way. And since the electric field is pointing this way, this queue must now be negative since the lottery fueled points towards the charges. And so the magnitude of queue is equal to e to our square over okay and employees and the new me too gives 3.5 times 10 to the mice thing cools. But really, we have to add a negative sign here because we found out that Catholic you was negatively charged, and so that completes the problem.

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