Three point chatges are placed onthe x axis .Acharge of+2micro c at the100cm mark .what are the magnitude and direction of the electrostatic force which acts on the charge at the origin
Well, well, well, looks like we have a shocking situation here! So, we have three charges on the x-axis and a charge at the origin. Let's call the charge at the origin "Charge-a-doodle-doo." Now, we've got a charge of +2 micro C at the 100 cm mark. Let's call this one "Chargezilla."
Now, to find the electrostatic force on our dear little "Charge-a-doodle-doo," we need to calculate the forces due to all the other charges. In this case, there's only one other charge, "Chargezilla," which is positively charged.
The magnitude of the electrostatic force between two charges is given by Coulomb's law:
F = k * (|q1 * q2| / r^2)
Where F is the force, k is Coulomb's constant (approximately 9 × 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Since "Charge-a-doodle-doo" and "Chargezilla" have opposite charges, the electrostatic force between them will be attractive. The force will be directed towards "Chargezilla" because opposites attract, just like magnets and my sense of humor!
Now, if we substitute in the values, we get:
F = 9 × 10^9 * (|q1 * q2| / r^2)
F = 9 × 10^9 * (|0 C * 2 × 10^-6 C| / (1 m)^2) [Remember, the charge at the origin is 0 C, so it exerts no force]
F = 9 × 10^9 * (2 × 10^-6 C / 1 m^2)
F = 9 × 10^9 * 2 × 10^-6 N
F = 18 × 10^3 N
So, the magnitude of the electrostatic force acting on "Charge-a-doodle-doo" is 18 × 10^3 Newtons, and the direction is towards "Chargezilla." It's like "Chargezilla" is a charging magnet, attracting everything towards it. Electrifying, isn't it?
To find the magnitude and direction of the electrostatic force acting on the charge at the origin due to the charge at the 100 cm mark, you can use Coulomb's Law.
Coulomb's Law states that the electrostatic force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Let's assume the charge at the origin is Q1 = 0 and the charge at the 100 cm mark is Q2 = +2 micro C (Coulombs).
The distance between the charges is r = 100 cm = 1 meter (since 1 meter = 100 cm).
Now let's calculate the magnitude of the electrostatic force (F) using Coulomb's Law:
F = (k * |Q1 * Q2|) / r^2
Where:
k is the electrostatic constant, which is approximately 9 x 10^9 Nm^2/C^2.
Substituting the values into the formula:
F = (9 * 10^9 Nm^2/C^2) * |0 * 2 * 10^(-6) C| / (1 m)^2
= (9 * 10^9 Nm^2/C^2) * 2 * 10^(-6) C
Now we can calculate the magnitude of the force:
F = 18 * 10^3 N
Therefore, the magnitude of the electrostatic force acting on the charge at the origin is 18,000 N.
To determine the direction of the force, we need to consider the signs of the charges. Since the charge at the 100 cm mark is positive (+2μC), and the charge at the origin is assumed to be neutral (0), the electrostatic force will act toward the positive charge. This means the direction of the electrostatic force is towards the positive x-axis.
To find the magnitude and direction of the electrostatic force acting on the charge at the origin, we need to consider the concept of Coulomb's Law, which states that the electrostatic force between two charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Let's assume the charges placed on the x-axis are labeled Q1, Q2, and Q3. Given that Q1 is located at the origin (0 cm) and has a charge of +2 micro C (micro Coulombs), and let's say Q2 and Q3 have unknown charges. The distance of Q1 from the charge at the 100 cm mark is 100 cm.
We can represent the distance as r and the force between Q1 and Q2 as F12. Since the charges are on the x-axis, the direction of the force would be along the x-axis as well. Let's denote it as F12(x).
Coulomb's Law equation is written as:
F12 = k * (Q1 * Q2) / r^2
Where:
- F12 is the force between Q1 and Q2
- k is the electrostatic constant (approximately equal to 9 x 10^9 Nm^2/C^2)
- Q1 and Q2 are the magnitudes of the charges
- r is the distance between the charges
In this case, Q1 is +2 micro C (2 x 10^-6 C), and r is 100 cm (or 1 m).
Substituting the values into the equation, we have:
F12 = (9 x 10^9 Nm^2/C^2) * (2 x 10^-6 C * Q2) / (1 m)^2
= 18 x 10^3 N * Q2
To find the magnitude and direction of the electrostatic force acting on the charge at the origin, we would need to know the value of Q2. Without that information, we cannot determine the exact magnitude and direction of the force.