A point charge, q= 400x 10^-9 C, is placed on the x-axis at the origin. What is the electric field produced at x = 25.0 cm²
in simple steps
To find the electric field produced at x = 25.0 cm² by a point charge q = 400x10^(-9) C at the origin, you can use Coulomb's law.
Coulomb's law equation states that the electric field (E) produced by a point charge (q) at a distance (r) from the charge is given by:
E = k * (q / r^2),
where k is the electrostatic constant and is equal to 9 * 10^9 Nm^2/C^2.
In this case, the distance (r) is 25.0 cm = 0.25 m.
Substituting the given values into the equation, we have:
E = (9 * 10^9 Nm^2/C^2) * (400 * 10^(-9) C) / (0.25 m)^2.
Simplifying the equation:
E = (9 * 400) / (0.25)^2 * 10^9 N/C.
E = (3600 / 0.0625) * 10^9 N/C.
E = 57600 * 10^9 N/C.
Therefore, the electric field produced at x = 25.0 cm² is 5.76 x 10^14 N/C.
To calculate the electric field produced by a point charge at any given point, follow these steps:
Step 1: Determine the distance between the point charge and the given point.
In this case, the point charge is located at the origin (x = 0) and the given point is at x = 25.0 cm². The distance between the two points is 25.0 cm.
Step 2: Convert the distance to meters.
Since the SI unit of electric charge is in Coulombs (C), it is essential to convert the distance from centimeters to meters. 1 meter = 100 centimeters.
Thus, the distance becomes 25.0 cm * (1 m / 100 cm) = 0.25 meters.
Step 3: Calculate the electric field using Coulomb's Law.
Coulomb's Law states that the electric field (E) generated by a point charge is given by the equation:
E = k * (q / r²)
Where:
- E represents the electric field.
- k is the Coulomb's constant, k = 8.99 × 10^9 N m²/C².
- q is the charge, which is 400 × 10^-9 C in this case.
- r is the distance between the charge and the point at which electric field is to be calculated.
Step 4: Plug the values into the equation and calculate the electric field.
E = (8.99 × 10^9 N m²/C²) * (400 × 10^-9 C) / (0.25 m)²
E = (8.99 × 10^9 N m²/C²) * (400 × 10^-9 C) / (0.25)²
E = (8.99 × 10^9 N m²/C²) * (400 × 10^-9 C) / 0.0625
E = (8.99 × 10^9 N m²/C²) * (0.0000004 C) / 0.0625
E ≈ 5.75 × 10^6 N/C
Therefore, the electric field at x = 25.0 cm² is approximately 5.75 × 10^6 N/C.
To find the electric field produced by a point charge at a specific point, you can use Coulomb's Law. Here are the steps to calculate the electric field at a position x = 25.0 cm:
Step 1: Define the variables:
- q: Point charge magnitude (given as 400x10^-9 C)
- r: Distance from the charge to the target point (25.0 cm or 0.25 m)
- k: Coulomb's constant (8.99x10^9 N·m^2/C^2)
Step 2: Convert all units to SI units:
- Convert cm to meters: 25.0 cm = 0.25 m
Step 3: Calculate the electric field using Coulomb's Law:
- E = k * (q / r^2)
Step 4: Plug in the values into the formula and calculate the electric field:
- E = (8.99x10^9 N·m^2/C^2) * (400x10^-9 C / (0.25 m)^2)
Step 5: Simplify and calculate the value:
- E = (8.99x10^9 N·m^2/C^2) * (0.16 C / 0.0625 m^2)
- E = 2.87136 * 10^5 N/C
So, the electric field produced by the point charge at x = 25.0 cm is approximately 2.87136 * 10^5 N/C.