Calculating Electric Field from a Bent Rod of Charge

In summary, the conversation discusses a rod with uniform linear charge density bent into an arc and placed at the origin of the axes. Part a determines the total charge on the rod, while part b determines the electric field at the center of the arc. The correct answer for part b is 2.3 × 106, which may have been incorrect due to a missing factor of R in the calculation. Part d asks for the force required to keep a proton at rest, using the answer from part b. Part e is not understood.
  • #1
musicfairy
101
0
semisemicircle.jpg


A rod of uniform linear charge density λ = +1.5 x 10 5 C/m is bent into an arc of radius R = 0.10 m. The arc is placed with its center at the origin of the axes shown above.
a. Determine the total charge on the rod.
b. Determine the magnitude and direction of the electric field at the center O of the arc.

A proton is now placed at point O and held in place. Ignore the effects of gravity in the rest of this problem.
d. Determine the magnitude and direction of the force that must be applied in order to keep the proton at rest.

My work for part a:

ssc1.jpg


Got this part right.

For part b:

ssc2.jpg


Didn't get this one right. I got 46722.8 for the answer while the correct answer is 2.3 × 106

What did I do wrong?

For part d I need the answer from part b. If I had it I would use F = qE.

I don't understand part e at all.

Please help me, especially on part b.
 
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  • #2
musicfairy said:
Didn't get this one right. I got 46722.8 for the answer while the correct answer is 2.3 × 106

What did I do wrong?
All I see wrong is a missing factor of R in your final answer. I assume that λ = 1.5 x 10^-5 C/m. If so, the correct answer follows.
 
  • #3
I got it. Thanks.
 

FAQ: Calculating Electric Field from a Bent Rod of Charge

1. What is the formula for calculating electric field from a bent rod of charge?

The formula for calculating electric field from a bent rod of charge is E = k * Q * (x + d) / (x^2 + d^2)^(3/2), where E is the electric field, k is the Coulomb's constant (9*10^9 N*m^2/C^2), Q is the charge of the rod, x is the distance from the point of observation to the end of the rod, and d is the distance between the two ends of the rod.

2. How do I determine the direction of the electric field from a bent rod of charge?

The direction of the electric field from a bent rod of charge is determined by the direction of the force it would exert on a positive test charge. The electric field lines always point away from positive charges and towards negative charges, so the direction of the electric field will be away from the rod if it has a positive charge and towards the rod if it has a negative charge.

3. Can I use the same formula to calculate the electric field at any point along the rod?

Yes, you can use the same formula to calculate the electric field at any point along the rod. However, the values for x and d may change depending on the specific point you are calculating the electric field at.

4. How does the electric field change as I move farther away from the bent rod of charge?

The electric field decreases as you move farther away from the bent rod of charge. This is because the electric field is inversely proportional to the square of the distance (x^2 + d^2) from the rod. As the distance increases, the denominator of the formula increases, resulting in a smaller electric field value.

5. Is there a maximum distance at which the electric field becomes negligible?

Yes, there is a maximum distance at which the electric field becomes negligible. This distance is typically considered to be three or four times the length of the rod. Beyond this distance, the electric field becomes very small and can be considered negligible for practical purposes.

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