Electric field at a point (point charge and semi-circle rod)

In summary, a thin semicircular rod with a total charge of +Q is placed as shown with a negative point charge of -Q at point C. The electric fields at point C due to the point charge and the rod are represented by Ep and Er, respectively. The magnitude of Ep is greater than the magnitude of Er since a segment charge on the rod can be treated as a point charge and thus has a greater electrical force. The magnitude of the net electric field at point C is equal to the magnitude of Ep since the point C lies on the electric field line between the fractional charge on the rod and the point charge. The net electric field is contributed by all charges on the rod (total of +Q) and can be represented
  • #1
AnonBae
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Homework Statement


A thin semicircular rod has a total charge +Q uniformly distributed along it. A negative point charge -Q is placed as shown. (Point C is equidistant from -Q and from all points on the rod.)
*Image Attached*
Let Ep and Er represent the electric fields at point C due to the point charge and the rod respectively.

a) Is the magnitude of Ep greater than, less than, or equal to the magnitude of Er? Explain.

b) Is the magnitude of the net electric field at point C greater than, lessthan, or equal to the magnitude of Ep? Explain.

Homework Equations


ΣE = Fe / q

The Attempt at a Solution


a. I am guessing the magnitude of Ep is greater than the magnitude of Er since we can treat a segment charge on the rod as a point charge, and thus the by the equation, the electric field is dependent on the charge. The fractional charge on the rod will produce a greater electrical force than the point charge does.
b. The magnitude of the net electric field is equal to the magnitude at Ep since the point C lies on the electric field line between point C and the fractional charge on the rod.
 

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  • #2
AnonBae said:
we can treat a segment charge on the rod as a point charge
In what sense, placed where, and of what magnitude?
AnonBae said:
The fractional charge on the rod
Why fractional?

For b, I don't think you are reading the question correctly.
 
  • #3
a. I do know that a fractional charge of +Q contributes to the electric field at point C since no other electric field lines cross through point C besides the one horizontal to point C. I am confused as to whether that fractional charge offsets its weak electric force by the formula for the electric field or it does not.

b. So, the net electric field is contributed by all charges on the rod (total of +Q) and the sum of the electric field from all those charges will equal the electric field Ep since they both converge at the same point?
 
  • #4
AnonBae said:
fractional charge of +Q contributes to the electric field at point C
I still don't know what you mean by a fractional charge here. Do you mean a continuously distributed charge? Or one infinitesimal element of the distributed charge? Or just some fraction less than 1 of Q?
AnonBae said:
no other electric field lines cross through point C besides the one horizontal to point C.
Except for the extreme ends, all parts of the rod generate a field which has a horizontal component at C.
Write an integral for the total field the rod produces at C.
 

FAQ: Electric field at a point (point charge and semi-circle rod)

What is an electric field?

An electric field is a physical field that surrounds charged particles and exerts a force on other charged particles within its vicinity. It is a vector quantity, meaning it has both magnitude and direction.

What is a point charge?

A point charge is a hypothetical charge that is concentrated at a single point in space. It has no physical size or shape, and its strength is described by its electric charge. It is often used in theoretical physics to simplify calculations.

How is the electric field at a point calculated for a point charge?

The electric field at a point due to a point charge is calculated using Coulomb's law, which states that the electric field strength is directly proportional to the magnitude of the point charge and inversely proportional to the square of the distance between the point charge and the point of interest.

What is a semi-circle rod?

A semi-circle rod is a physical object that has a curved shape resembling half of a circle. It can be used as a model to represent real-life objects, such as wires or rods, in certain physics problems.

How is the electric field at a point calculated for a semi-circle rod?

The electric field at a point due to a semi-circle rod is calculated by breaking the rod into small segments and using the principle of superposition to add up the individual electric fields created by each segment at the point of interest. This calculation can become quite complex, but it follows the same principles as calculating the electric field for a point charge.

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