Particle 1 and 2 of charge q1 = q2 = +3.3*10-19 C are on the y-axis at distance d = 17cm from the origin. Particle 3 of charge q3 = 6.4*10-19 C is moved gradually along the x-axis from x = 0 to x = 5.0cm. At what values of x will the magnitude of the electrostatic force on the third particle from the other two particle be
1) Minimum
2) Maximum
To find the values of x at which the magnitude of the electrostatic force on the third particle is minimum and maximum, we can use the principle of superposition of forces.
The electrostatic force between two charged particles is given by Coulomb's Law:
F = k * (|q1*q2| / r^2)
Where:
- F is the magnitude of the electrostatic force
- k is the electrostatic constant (k = 8.99 * 10^9 N m^2/C^2)
- q1 and q2 are the charges of the two particles
- r is the distance between the two particles
Let's start by finding the electrostatic force between Particle 1 (q1) and Particle 3 (q3). The distance between them is given by the distance formula:
r = √((x - 0)^2 + (0 - d)^2)
Since Particle 1 and Particle 2 have the same charge and are equidistant from Particle 3, the magnitude of the electrostatic force between Particle 2 (q2) and Particle 3 (q3) will be the same.
Now, we need to find the minimum and maximum values of the electrostatic force. To do this, we'll take the derivative of the force function with respect to x and equate it to zero.
1) To find the value of x at which the force is minimum:
- Take the derivative ∂F/∂x
- Set it to zero and solve for x
2) To find the value of x at which the force is maximum:
- Take the derivative ∂F/∂x
- Set it equal to zero and check the sign of the second derivative ∂^2F/∂x^2 to determine if it is a maximum or minimum point
- Determine the x values where the second derivative changes sign, and evaluate F at those points to find the maximum
By following these steps, we can find the values of x at which the electrostatic force on the third particle is minimum and maximum.