A thin rod L = 9.0 cm long is uniformly charged and has a total charge of 4.4 nC. Find the magnitude of the electric field at a point P located at a distance R = 13.5 cm from the center of the rod when:
(a) The point P lies along the axis of the rod
Electric field =___kN/C
(b) The point P lies perpendicularly to the axis of the rod
Electric field =___kN/C
To find the magnitude of the electric field at a point P located at a distance R from the center of a uniformly charged rod, we can use the formula for the electric field due to a charged rod:
E = (k * q) / (2πε * L * R)
where:
- E is the magnitude of the electric field at point P,
- k is the Coulomb's constant (9.0 x 10^9 N m^2/C^2),
- q is the total charge on the rod (in this case, 4.4 nC = 4.4 x 10^(-9) C),
- ε is the permittivity of free space (8.85 x 10^(-12) C^2/N m^2),
- L is the length of the rod (9.0 cm = 0.09 m),
- R is the distance from the center of the rod to point P.
Now, let's calculate the electric field at point P for both cases:
(a) When the point P lies along the axis of the rod:
In this case, the distance from the center of the rod to point P is R = 13.5 cm = 0.135 m.
Using the formula, we can substitute the given values:
E = (k * q) / (2πε * L * R)
= (9.0 x 10^9 N m^2/C^2 * 4.4 x 10^(-9) C) / (2π * 8.85 x 10^(-12) C^2/N m^2 * 0.09 m * 0.135 m)
Solving this equation will give us the value of the electric field in kN/C.
(b) When the point P lies perpendicularly to the axis of the rod:
In this case, the distance from the center of the rod to point P is also R = 13.5 cm = 0.135 m.
Using the same formula as before, we can substitute the given values:
E = (k * q) / (2πε * L * R)
= (9.0 x 10^9 N m^2/C^2 * 4.4 x 10^(-9) C) / (2π * 8.85 x 10^(-12) C^2/N m^2 * 0.09 m * 0.135 m)
Again, solving this equation will give us the value of the electric field in kN/C.