Electric Field at the End of a Line of Charge

In summary, a charged rod of length 7.10 m with a charge density of λ=ax^2 and a=−20.2 μC/m^3 lies centered on the x axis. The x component of the electric field at a point on the x-axis 3.70 m from the end of the rod can be found using Coulomb's Law, which requires integrating over the charge from -L/2 to L/2 and taking into account the distance from the dq's to the point P.
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bhdmia
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Field at End of Line of Charge 2

A charged rod of length L=7.10 m lies centered on the x axis as shown. The rod has a charge density which varies according to λ=ax^2 where a=−20.2 μC/m^3 .

What is the x component of the electric field at a point on the x-axis a distance of D=3.70 m from the end of the rod?
media%2F71b%2F71ba0d9b-0e30-4c4b-8021-8ce735eb4fa9%2Fphp3k5qvx.png
Relevant equations: Coulomb's Law - E=kQ/r^2The attempt at a solution: Ok, so part I of this problem was to calculate the total charge of the rod, which I figured out easily enough. Part II, as stated above, is to find the electric field at some point P along the axis of the line of charge. Here's my attempted solution:

E = ∫ (kdQ/r^2)*<i> where dQ=ax^2dx where r=x. The x^2 on top and x^2 on bottom cancel out so you just end up integrating dx with bounds (D+L) and (L) and multiply by k and a. That didn't work, so I tried the equation with <xi> for the r vector and that didn't work either. I can't figure out what I'm doing wrong. Help!
 
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You need to integrate over the charge, from -L/2 to L/2. But the distance from the dq's to the point P is not the same as the x that "scans" the rod.
 

Related to Electric Field at the End of a Line of Charge

What is an electric field at the end of a line of charge?

An electric field at the end of a line of charge refers to the strength and direction of the electric field surrounding a single charged object or line of charged particles. It is a vector quantity that describes the force per unit charge experienced by other charged particles in the vicinity.

How is the electric field at the end of a line of charge calculated?

The electric field at the end of a line of charge is calculated using Coulomb's Law, which states that the electric field is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the charged object and the point where the electric field is being measured.

What is the direction of the electric field at the end of a line of charge?

The direction of the electric field at the end of a line of charge is dependent on the charge of the object. If the object is positively charged, the electric field will point away from the object. If the object is negatively charged, the electric field will point towards the object.

How does the electric field at the end of a line of charge change with distance?

The electric field at the end of a line of charge follows an inverse square relationship with distance. This means that as the distance from the charged object increases, the strength of the electric field decreases exponentially. This relationship holds true as long as the charge remains constant.

Can the electric field at the end of a line of charge be shielded or cancelled out?

Yes, the electric field at the end of a line of charge can be shielded or cancelled out by introducing an opposite charge nearby. This is known as electrostatic shielding and is commonly used in electronic devices to prevent interference from external electric fields.

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