There is a rod that is 50cm long and has a radius of 1cm that carries a charge of 2uC distributed uniformly over its length. What would be the value of the magnitude of the electric field. (a) 4.0 mm from the rod surface, not either end
So far I got E1/4density-2pie0r or
E= 2(9.10^9)(8*10^-6) what do i do after that?
I do not understand your formula.
because the distance from the rod is much less than the rod length, assume it is an infinte rod.
E= 2k*lambda/r
r will be the radius of the rod plus the distance from the surface. r=0.0104m
lamda is 2uC/.5 micro coulombs/meter.
www.phys.uri.edu/~gerhard/PHY204/tsl31.pdf -
To find the magnitude of the electric field at a distance of 4.0 mm from the rod surface, you can use Coulomb's Law combined with the principle of superposition. Here's how you can proceed:
1. Determine the charge density (charge per unit length) of the rod:
The rod carries a charge of 2 μC distributed uniformly over its length of 50 cm. Let's convert the length to meters:
Length of the rod, l = 50 cm = 0.5 m
Charge, Q = 2 μC = 2 × 10^-6 C
Charge density, λ = Q / l = (2 × 10^-6 C) / (0.5 m) = 4 × 10^-6 C/m
2. Apply Coulomb's Law to calculate the electric field contribution from a small element of the rod:
Consider a small element of length dl at a distance r from the rod surface. The electric field contribution due to this small element is given by:
dE = (kdλ) / r^2
Where k is Coulomb's constant, k = (1 / 4πε0), and ε0 is the permittivity of free space (ε0 = 8.85 × 10^-12 C^2/(N·m^2)).
3. Integrate over the entire length of the rod to find the total electric field:
To calculate the electric field at a distance away from the rod, we need to integrate the electric field contributions from all elements of the rod. Since the rod has charge distributed uniformly, we can integrate the electric field equation over the entire length of the rod.
The electric field at a distance r from the rod's surface is given by:
E = (1 / 4πε0) × ∫[λ / r^2]dl
Integrating from -l/2 to l/2, where l is the total length of the rod.
4. Perform the integration and evaluate the equation:
E = (1 / 4πε0) × ∫[(4 × 10^-6 / r^2) dl]
Integrating (4 × 10^-6 / r^2) with respect to dl from -l/2 to l/2, you should find that this part equals 1.
Therefore, the equation simplifies to:
E = (1 / 4πε0)
5. Evaluate the equation using the given values:
The value of ε0 is given as 8.85 × 10^-12 C^2/(N·m^2).
Plug in this value to find the magnitude of the electric field at 4.0 mm from the rod's surface.
By following these steps, you should be able to determine the magnitude of the electric field at the specified distance from the rod's surface.