Finding the magnitude of the eletric field of a uniformly charged rod.

[ILoveCollege]

Homework Statement

"A rod of 13.1 cm long is uniformly charged and has a total charge of -23.2 micro coulombs. Determine the magnitude of the electric field along the axis of the rod at a point 52.1575 cm from the center of the rod. The Coulomb constant is 8.98755e9 N M^2/C^2. Answer in units of N/C"
I'm lost on how to go about solving this. I've tried just doing E=KQ/R^2 with R being 52.1575 cm and I tried E= KQ/(R^2+X^2)^2/3 with X= 52.1575 and R=13.1 but that's wrong to

 

[rl.bhat]

Total charge on the rod is given. Length of the rod L is given. Find the linear charge density λ.Take a small element dx of the rod at a distance x from the center. Charge on this element dq = λ*dx. Let its distance from the point where the electric field is required is (d - x) where d is the distance of the point from he center.
Field due to dq at P is
dE = k*λ*dx/(d-x)^2. Find the integration between the limits x = +L/2 to -L/2

 

[kerimek]

apparently

I would first clarify the given information and variables in the problem. The length of the rod, 13.1 cm, and the total charge, -23.2 micro coulombs, are given. The distance from the center of the rod to the point where the electric field is being measured, 52.1575 cm, is also given. Additionally, the Coulomb constant, 8.98755e9 N M^2/C^2, is provided.

To solve for the magnitude of the electric field, I would use the formula E = kQ/r^2, where k is the Coulomb constant, Q is the total charge of the rod, and r is the distance from the center of the rod to the point where the electric field is being measured. Plugging in the given values, we get:

E = (8.98755e9 N M^2/C^2)(-23.2 micro coulombs) / (52.1575 cm)^2

Converting the units to meters, we get:

E = (8.98755e9 N M^2/C^2)(-23.2e-6 C) / (0.521575 m)^2

Simplifying, we get:

E = -2.88e4 N/C

Therefore, the magnitude of the electric field along the axis of the rod at a point 52.1575 cm from the center of the rod is 2.88e4 N/C.

If the calculated answer does not match the expected answer, I would double check my calculations and make sure all units are consistent. I would also consider if there are any other factors or assumptions that need to be taken into account, such as the size or shape of the rod. If necessary, I may consult with a colleague or refer to additional resources for assistance.