A point charge, q= 400x 10 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 by a point charge, you can use Coulomb's law equation:
E = k * (q / r^2)
where:
E is the electric field
k is the electrostatic constant, approximately equal to 9 x 10^9 Nm^2/C^2
q is the charge
r is the distance from the charge
In this case, the charge q is given as 400 x 10 C, which is equal to 400 Coulombs.
The distance r is given as 25.0 cm, which is equal to 0.25 meters.
Plugging these values into the equation, we have:
E = (9 x 10^9 Nm^2/C^2) * (400 C / (0.25 m)^2)
Simplifying the equation:
E = (9 x 10^9 Nm^2/C^2) * (400 C / 0.0625 m^2)
E = (9 x 10^9 Nm^2/C^2) * (6400 C / m^2)
E = (9 x 10^9 N * 6400) / Cm
E = 57.6 x 10^9 N/C
Therefore, the electric field produced at x = 25.0 cm^2 is 57.6 x 10^9 N/C.
To calculate the electric field produced by a point charge at a specific location, we can use Coulomb's law. Here are the steps:
Step 1: Write down Coulomb's law equation.
Coulomb's law states that the electric field produced by a point charge can be calculated using the equation:
E = k * (q / r^2)
where E is the electric field, k is the electrostatic constant, q is the charge of the point charge, and r is the distance between the point charge and the location where we want to calculate the field.
Step 2: Define the given values.
In this case, we have a point charge q = 400 x 10 C (Coulombs) and the location at x = 25.0 cm. We need to convert this distance to meters, so x = 25.0 cm = 0.25 m. The electrostatic constant is given by k = (9 x 10^9 N*m^2/C^2).
Step 3: Calculate the electric field.
Substitute the given values into the Coulomb's law equation:
E = (9 x 10^9 N*m^2/C^2) * (400 x 10 C) / (0.25 m)^2
Step 4: Simplify the equation and calculate.
First, square the distance:
E = (9 x 10^9 N*m^2/C^2) * (400 x 10 C) / (0.25)^2
E = (9 x 10^9 N*m^2/C^2) * (400 x 10 C) / 0.0625
Next, multiply the charge and the constant:
E = (9 x 10^9 N*m^2/C^2) * (400 x 10 C) / 0.0625
E = (9 x 10^9 N*m^2/C^2) * (400 x 10 C) * 16
Finally, calculate the electric field:
E = (9 x 10^9 N*m^2/C^2) * (400 x 10 C) * 16
E = 5.76 x 10^13 N/C
Therefore, the electric field produced at x = 25.0 cm is 5.76 x 10^13 N/C.
To find the electric field produced by the point charge at a certain point, you can follow these steps:
Step 1: Determine the distance between the point charge and the point where you want to find the electric field. In this case, the distance is given as x = 25.0 cm.
Step 2: Remember that the electric field produced by a point charge is given by the equation E = k * (q / r^2), where k is the electrostatic constant (k = 9.0 x 10^9 Nm²/C²), q is the charge, and r is the distance.
Step 3: Substitute the given values into the equation: E = (9.0 x 10^9 Nm²/C²) * (400 x 10^-10 C) / (0.25 m)².
Step 4: Simplify the equation: E = (9.0 x 10^9 Nm²/C²) * (400 x 10^-10 C) / (0.0625 m²).
Step 5: Calculate the numerator separately: (9.0 x 10^9 Nm²/C²) * (400 x 10^-10 C) = 3.6 Nm²/C.
Step 6: Calculate the denominator separately: (0.0625 m²).
Step 7: Divide the numerator by the denominator: E = (3.6 Nm²/C) / (0.0625 m²).
Step 8: Simplify the equation: E = 57.6 N/C.
Therefore, the electric field produced at x = 25.0 cm from the point charge is 57.6 N/C.