Electric Fields and Forces in water

In summary, the question asks to determine the electric field, electric potential, and electric force experienced by a positive and negative charge placed between two negative charges in water. Using the equations E = kq/Kr^2, V = kq1/Kr1 + kq2/Kr2, and F = qE, the electric field and potential at the position of the positive and negative charges can be calculated. The electric force experienced by the charges is found by multiplying the charge with the electric field. It is important to consider the sign of the charge when determining the direction of the force.
  • #1
km7
1
0

Homework Statement



Two negative charges of -1.0x10^-6 C each are placed in water and separated by a distance of 0.10m. A positive charge of 1.0x10^-8 C is placed exactly midway between the two negative charges. Determine:

a) the electric field (magnitude and direction) and electric potential at the position of the positive charge

b) the electric field (magnitude and direction) and electric potential at the position of either negative charge

c) the electric force (magnitude and direction) experienced by the positive charge

d) the electric force (magnitude and direction) experienced by either negative charge


Homework Equations



E = kq/Kr^2
V = kq1/Kr1 + kq2/Kr2
F = Eq ?

The Attempt at a Solution



let q1 be negative charge on the left and q2 be negative charge on the right
let q0 be positive charge that is in between q1 an q2

a)
E total = E1 + E2
= (- kq1/Kr1^2) + (+ kq2/Kr2^2) = 0 N/C
V = kq1/Kr1 + kq2/Kr2 = - 4.47 x 10^3 V

b)
E total = E0 + E2
= (+ kq0/Kr0^2) + (+ kq2/Kr2^2) = + 1.1626 x 10^4 N/C (direction ?)
V = kq0/Kr + kq2/Kr = - 1.09 x 10^3 V (first r = 0.05m, second r = 0.10 m ?)

c) and d)
F = Eq ?
F = kq1q1/Kr^2 ?



I tried solving them and got answers to a and b but not to c and d. I am confused when to include - or + sign in front of E, V, F, and q (do not understand what those signs mean exactly .. :[ ). Maybe I am not understanding the question correctly?

It would be great if anyone can explain them to me (basic concepts).

Thank you!
 
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  • #2
Welcome to PF!

Hi km7! Welcome to PF! :smile:
km7 said:
… c) the electric force (magnitude and direction) experienced by the positive charge

d) the electric force (magnitude and direction) experienced by either negative charge

F = Eq ?

I tried solving them and got answers to a and b but not to c and d. I am confused when to include - or + sign in front of E, V, F, and q (do not understand what those signs mean exactly .. :[ ). Maybe I am not understanding the question correctly?

Yes, F = qE is the correct equation …

the "Lorentz force" of an electric field E on a charge q is qE

in other words, the force is parallel to the field, and is multiplied by q (so if q is positive, then it's in the same direction, while if q is negative, then it's in the opposite direction) :smile:
 
  • #3




The electric field in water is a vector quantity that describes the strength and direction of the force experienced by a charged particle placed in the water. It is calculated using the equation E = kq/r^2, where k is the Coulomb's constant, q is the charge of the particle, and r is the distance from the particle to the source of the field.

In this homework problem, we have two negative charges (q1 and q2) placed in water and separated by a distance of 0.10m. A positive charge (q0) is placed exactly midway between the two negative charges. We are asked to determine the electric field, electric potential, and electric force experienced by the positive charge and either of the negative charges.

a) To find the electric field at the position of the positive charge, we can use the equation E = kq/r^2. Since the positive charge is equidistant from the two negative charges, the electric fields from each of the negative charges will cancel out, resulting in a net electric field of 0 N/C. This means that the positive charge will not experience any force in this position. However, the electric potential at this point can be calculated using the equation V = kq1/r1 + kq2/r2. Plugging in the values, we get a potential of -4.47 x 10^3 V.

b) To find the electric field and potential at the position of either negative charge, we can use the same equations as in part a. However, since the negative charges have the same magnitude and are placed at equal distances, the electric field and potential will also be equal and opposite at these positions. This means that the electric field will be +1.1626 x 10^4 N/C and the potential will be -1.09 x 10^3 V.

c) To find the electric force experienced by the positive charge, we can use the equation F = Eq. Plugging in the values, we get a force of 9 x 10^-6 N. The direction of this force will be towards the negative charges.

d) Similarly, to find the electric force experienced by either negative charge, we can use the same equation as in part c. Plugging in the values, we get a force of 9 x 10^-6 N. The direction of this force will be away from the positive charge.

It is important to note that
 

What is an electric field?

An electric field is a region in which an electric charge experiences a force. It is represented by a vector that points in the direction of the force that would be exerted on a positive charge placed at that point.

How do electric fields and forces work in water?

In water, electric fields and forces are caused by the presence of ions, which are charged particles. These ions can be naturally occurring or introduced through the addition of substances such as salt. The movement of these ions creates an electric field, and the force exerted on a charged particle in the field is directly proportional to the strength of the field.

What is the relationship between electric fields and electric potential in water?

Electric potential is a measure of the energy that a charged particle would have at a specific point in an electric field. In water, the electric potential is directly related to the strength of the electric field and the distance between the charged particles. The stronger the electric field, the higher the electric potential will be.

Can electric fields and forces in water be manipulated?

Yes, electric fields and forces in water can be manipulated through the use of external electric fields or by altering the concentration of ions in the water. This manipulation can be used for various purposes, such as purifying water or powering devices.

What are some real-world applications of electric fields and forces in water?

Electric fields and forces in water have many practical applications, such as in water purification systems, electrochemical processes, and the functioning of living organisms. They are also used in technologies such as batteries, capacitors, and sensors.

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