A very long uniform line of charge has a charge per unit length of 4.82 uC/m

In summary, there are two long uniform lines of charge, one with a charge per unit length of 4.82 uC/m and the other with a charge per unit length of -2.46 uC/m, both parallel to the x-axis. The magnitude of the net electric field at point y2= 0.202 m on the y-axis is 3.14 N/C and the direction is along the -y-axis. Similarly, at point y3= 0.608 m on the y-axis, the magnitude of the net electric field is 9.42 N/C and the direction is also along the -y-axis.
  • #1
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Homework Statement


A very long uniform line of charge has charge per unit length 4.82 uC/m and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.46 uC/m and is parallel to the x-axis at y1= 0.418
1-)What is the magnitude of the net electric field at point y2= 0.202 m on the y-axis?
2-)What is the direction of the net electric field at point y2= 0.202 m on the y-axis?
-y-axis
+y-axis
3-)What is the magnitude of the net electric field at point y3= 0.608 m on the y-axis?
4-)What is the direction of the net electric field at point y3 = 0.608 m on the y-axis?
-y-axis
+y-axis


Homework Equations



EA=PA/epsilon-nought
E=kq/r2


The Attempt at a Solution



I don't really know where to start.
At first I tried to do E=(k*dq)/r^2 = k(4.82e-6)/(x^2+.202^2)
But then realized that I don't have a definite integral. Then I tried to use E=(kq1/r1)+(kq2/r2)... but the answer was incorrect. Anyone know how to start this problem..?
 
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  • #3


I would approach this problem by using the equation for the electric field due to a line of charge, which is given by:

E = (kλ)/r

Where E is the electric field, k is the Coulomb's constant (8.99x10^9 Nm^2/C^2), λ is the charge per unit length, and r is the distance from the line of charge.

1) To find the magnitude of the net electric field at point y2= 0.202 m on the y-axis, we can use the equation above and calculate the electric fields due to each line of charge separately. Since the first line of charge is located on the x-axis, the distance from the point to this line is simply 0.202 m. Therefore, the electric field due to this line is:

E1 = (kλ1)/r1 = (8.99x10^9 Nm^2/C^2)(4.82x10^-6 C/m)/(0.202 m) = 213.4 N/C

Similarly, for the second line of charge, the distance from the point to this line is:

r2 = √(y2^2 + y1^2) = √((0.202 m)^2 + (0.418 m)^2) = 0.468 m

Therefore, the electric field due to this line is:

E2 = (kλ2)/r2 = (8.99x10^9 Nm^2/C^2)(-2.46x10^-6 C/m)/(0.468 m) = -41.6 N/C

Now, we can find the total electric field at point y2 by adding these two fields together:

E = E1 + E2 = 213.4 N/C - 41.6 N/C = 171.8 N/C

Therefore, the magnitude of the net electric field at point y2= 0.202 m on the y-axis is 171.8 N/C.

2) To find the direction of the net electric field at this point, we can look at the direction of each individual electric field. E1 is directed along the positive y-axis, while E2 is directed along the negative y-axis. Since E1 is larger than E2, the overall direction of the net electric field will be in the direction of E1, which
 

Related to A very long uniform line of charge has a charge per unit length of 4.82 uC/m

1. What is a uniform line of charge?

A uniform line of charge is a theoretical concept in physics where a long line of charge is evenly distributed along its length. This means that the charge density, or amount of charge per unit length, remains constant throughout the line.

2. How is charge per unit length measured?

Charge per unit length is measured in coulombs per meter (C/m) or microcoulombs per meter (uC/m). It represents the amount of charge that exists in a specific length of the line of charge. In the given scenario, the charge per unit length is 4.82 uC/m.

3. What is the unit of charge?

The unit of charge is the coulomb (C). It is a fundamental unit in the International System of Units (SI) and is defined as the amount of charge transported by a constant current of one ampere in one second.

4. How does the charge per unit length affect the electric field?

The charge per unit length of a line of charge affects the electric field around it. The electric field strength is directly proportional to the charge per unit length, meaning that as the charge per unit length increases, the electric field strength also increases. This relationship is described by Coulomb's Law.

5. Is the charge per unit length constant for all types of lines of charge?

No, the charge per unit length can vary for different types of lines of charge. For example, a non-uniform line of charge where the charge density changes along its length will have varying charge per unit length. Additionally, different materials can also have different charge per unit length for the same line of charge depending on their conductivity.

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