a point charge placed at the origin. Calculate eletric field at a point 2.0m from the Z axis.
To calculate the electric field at a point 2.0m from the Z-axis due to a point charge at the origin, we can use Coulomb's Law and the concept of superposition. Here are the steps to calculate:
1. Determine the magnitude of the electric field due to the point charge at the origin using Coulomb's Law:
- Coulomb's Law states that the electric field created by a point charge is directly proportional to the magnitude of the charge (Q) and inversely proportional to the square of the distance (r) between the charge and the point where the electric field is measured.
- The formula for the magnitude of the electric field (E) is: E = k * (Q / r^2), where k is the electrostatic constant (k = 9 × 10^9 N m^2/C^2).
2. Calculate the distance (r) between the point charge at the origin and the point where the electric field is being measured:
- In this case, the distance is given as 2.0m from the Z-axis.
3. Plug in the values into the equation to calculate the electric field:
- E = k * (Q / r^2)
- Substitute the values of k = 9 × 10^9 N m^2/C^2, Q (charge at the origin), and r (distance from the Z-axis) into the equation.
- Calculate and obtain the value of E, which will give the magnitude of the electric field at the given point.
Note: The direction of the electric field will be radially outward or inward from the charge, depending on its sign (positive or negative).
Remember to use appropriate units throughout the calculation to obtain the correct numerical answer for the electric field at the specified point.