Electric field of Continuous charge Distribution

In summary, a semicircle of positive charge with radius R = 57.8 cm is described by the expression λ(θ) = λ0cosθ, and has a total charge of 13.2 µC. Part (a) requires calculating the constant λ0, which has a value of 1.14e-05 C/m. Part (b) involves finding the total force on a charge of 3.11 µC placed at the center of curvature, which requires setting up an integral over the range of θ.
  • #1
amninder15
19
0
A line of positive charge is formed into a semicircle of radius R = 57.8 cm, as shown in the figure below. (The figure is a semicircle above the x-axis with angle θ measured from positive y
axis centred at the origin)

The charge per unit length along the semicircle is described by the expression λ(θ) = λ0cosθ. The total charge on the semicircle is 13.2 µC.
(a) Calculate the value of the constant λ0.
(b) Calculate the total force on a charge of 3.11 µC placed at the center of curvature.

I did part a i found the answer 1.14e-05 C/m. but for part (b) i can't seem to setup the integral

any help would be appreciated.
 
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  • #2
You need to find the force due to a small part of the semi-circle at angle θ which is inside the arc Rdθ, then integrate that over the whole range of θ.

Where do you get stuck?
 

FAQ: Electric field of Continuous charge Distribution

What is an electric field?

An electric field is a physical field that surrounds an electrically charged particle or group of particles. It is a vector field, meaning it has both magnitude and direction, and it exerts a force on other charged particles within its range.

How is the electric field of a continuous charge distribution calculated?

The electric field of a continuous charge distribution is calculated using Coulomb's law and the principle of superposition. This means that the electric field at any point is the vector sum of the individual electric fields produced by each charged particle in the distribution.

What is the difference between a point charge and a continuous charge distribution?

A point charge is a single, isolated charge whereas a continuous charge distribution is a collection of many charges distributed over a certain area or volume. The electric field of a point charge is a simple radial field, while the electric field of a continuous charge distribution can have more complex shapes and variations.

How does the electric field of a continuous charge distribution affect other charges?

The electric field of a continuous charge distribution exerts a force on other charges within its range. The direction of this force is determined by the direction of the electric field, and the magnitude of the force is determined by the charge and distance of the affected charge from the distribution.

Can the electric field of a continuous charge distribution be negative?

Yes, the electric field of a continuous charge distribution can be negative. This simply means that the direction of the electric field is opposite to the direction of the force it exerts on other charges. It does not mean that the electric field itself is negative, as electric fields are always positive in magnitude.

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