Consider a “semi-infinite” nonconducting rod
(that extends infinitely to the right only) and has a
uniform charge density. Calculate the magnitude
and direction of the electric field at the point, P,
which is a distance of R away from the edge of
the rod.
Does the angle of the electric field, relative to the
orientation of the rod, change as R is increased?
To calculate the magnitude and direction of the electric field at point P, which is a distance R away from the edge of the rod, we can use the formula for the electric field produced by an infinitely long rod with uniform charge density.
Let's break down the steps to find the answer:
1. Determine the charge density:
The problem states that the rod has a uniform charge density, which we can denote as λ (lambda). The charge density represents the amount of charge per unit length along the rod.
2. Calculate the electric field at point P:
The electric field at point P can be found using the formula for the electric field produced by an infinite line of charge:
E = k * λ / R
In this formula, E represents the magnitude of the electric field, k is Coulomb's constant (k = 9 x 10^9 N m^2/C^2), λ is the charge density, and R is the distance from the edge of the rod to point P.
3. Determine the direction of the electric field:
The direction of the electric field can be determined by the direction the field lines point in. In the case of an infinitely long rod, the electric field lines will be directed radially outward from the rod, perpendicular to the rod's length. So the field lines will be perpendicular to the rod's orientation.
4. Analyze the relationship between the angle of the electric field and R:
As R is increased, the angle of the electric field relative to the orientation of the rod remains constant. Since the electric field lines are perpendicular to the rod's length, the angle between the field lines and the orientation of the rod does not change regardless of the distance R.
In summary, the magnitude of the electric field at point P is given by E = k * λ / R, and the angle of the electric field relative to the orientation of the rod remains constant, regardless of the distance R.