Electric field on the axis of a ring-shaped charged conductor

  • #1
yashboi123
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Homework Statement
A ring-shaped conductor with radius a = 2.20 cm has a total positive charge Q = 0.130 nC uniformly distributed around it
Relevant Equations
E = F/q
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Hello. I was wondering why do we not multiply cos(alpha) by 2. I believe we should do this since the y-components of the electric field cancel out, meaning there would be 2 x-components of the electric field(at least I think so). Currently, this derivation/answer only considers one horizontal component, not the other half.
 
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  • #2
How does it only consider one horizontal component when the integration is from ##0## to ##2 \pi##?

The integration bounds take care of this “doubling up effect”.

If you did it from ##0## to ##\pi## you would certainly have to multiply by 2 at the end.
 
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1. What is the formula for the electric field on the axis of a ring-shaped charged conductor?

The formula for the electric field on the axis of a ring-shaped charged conductor is E = kqz / (z^2 + R^2)^(3/2), where E is the electric field, k is the Coulomb constant, q is the charge of the ring, z is the distance from the center of the ring to the point where the electric field is being calculated, and R is the radius of the ring.

2. How does the electric field vary along the axis of a ring-shaped charged conductor?

The electric field on the axis of a ring-shaped charged conductor varies inversely with the cube of the distance from the center of the ring. This means that as you move further away from the ring, the electric field strength decreases rapidly.

3. What is the direction of the electric field on the axis of a ring-shaped charged conductor?

The direction of the electric field on the axis of a ring-shaped charged conductor is along the axis of the ring, pointing away from the ring if the charge is positive and towards the ring if the charge is negative.

4. How does the radius of the ring affect the electric field on its axis?

The radius of the ring affects the electric field on its axis by influencing the strength of the electric field. A larger radius will result in a weaker electric field, while a smaller radius will result in a stronger electric field.

5. Can the electric field on the axis of a ring-shaped charged conductor ever be zero?

Yes, the electric field on the axis of a ring-shaped charged conductor can be zero at certain points. These points are located at a distance z = R / sqrt(2) from the center of the ring, where the electric field contributions from opposite sides of the ring cancel each other out.

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