Finding E-field at a point away from a line charge

To determine the x-component, you can use the formula Ex= (Q/L)/(4ε0a). In summary, the problem is to calculate the x-component and y-component of the E-field at a point P, a distance 'a' from the origin on the positive y-axis, for a line charge with uniform linear charge density Lambda along the x-axis extending from -∞ to 0. The formula used is dE= (k*dq/r^2)* r(hat), with the x-component being Ex= (Q/L)/(4ε0a) and the y-component being Ey= (Q/L)/(4ε0a). There is an x-component at point P, even though the point lies on the y
  • #1
Geophyx
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Homework Statement


A line charge with a uniform linear charge density Lambda lies along the x-axis and extends from -∞ to 0. Determine the X-component, and Y-component of the E-field at a point P, a distance 'a' from the origin on the positive y-axis.

Homework Equations


dE= (k*dq/r^2)* r(hat)

The Attempt at a Solution


I'm getting tripped up on the limits of integration. Is there an x-component of the E-field at point P, even though the point lies on the Y-axis? I was able to calculate the Y-component and got Ey= (Q/L)/(4ε0a)
 
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  • #2
Geophyx said:

Homework Statement


A line charge with a uniform linear charge density Lambda lies along the x-axis and extends from -∞ to 0. Determine the X-component, and Y-component of the E-field at a point P, a distance 'a' from the origin on the positive y-axis.

Homework Equations


dE= (k*dq/r^2)* r(hat)

The Attempt at a Solution


I'm getting tripped up on the limits of integration. Is there an x-component of the E-field at point P, even though the point lies on the Y-axis? I was able to calculate the Y-component and got Ey= (Q/L)/(4ε0a)
Yes, there is an x-component.
 

Related to Finding E-field at a point away from a line charge

1. What is a line charge?

A line charge is an infinitely long, thin line that has a uniform charge distribution along its length. It is represented by the symbol λ and is measured in coulombs per meter (C/m).

2. How is the electric field (E-field) calculated at a point away from a line charge?

The E-field at a point away from a line charge can be calculated using the formula E = kλ/r, where k is the Coulomb's constant (9x10^9 Nm^2/C^2), λ is the charge density of the line charge, and r is the distance from the point to the line charge.

3. Is the E-field stronger or weaker closer to a line charge?

The E-field is stronger closer to a line charge and weaker farther away. This is because the E-field is inversely proportional to the distance from the line charge, according to the formula E = kλ/r.

4. Can the E-field at a point away from a line charge be negative?

Yes, the E-field at a point away from a line charge can be negative. This indicates the direction of the field, which can be either towards or away from the line charge depending on the sign of the charge density λ.

5. Can the E-field at a point away from a line charge be affected by other charges?

Yes, the E-field at a point away from a line charge can be affected by other charges. This is because electric fields are vector quantities and can be influenced by multiple charges in the surrounding area. In this case, the E-field at a point would be the vector sum of the individual E-fields from each charge.

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