A charge of +9.0 nC and a charge of +4.0 nC
are separated by 50.0 cm.
Find the equilibrium position for a −1.0 nC
charge as a distance from the first charge. The
Coulomb charge is 8.98755 × 109 N · m2
/C
2
.
Answer in units of cm.
To find the equilibrium position for a -1.0 nC charge, we can use Coulomb's Law.
Coulomb's Law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It can be expressed as:
F = (k * (q1 * q2)) / r^2
Where:
F is the force between the charges
k is the Coulomb's constant (k = 8.98755 × 10^9 N · m^2/C^2)
q1 and q2 are the charges
r is the distance between the charges
In this case, the first charge is +9.0 nC and the second charge is +4.0 nC. The distance between them is given as 50.0 cm.
Now, we need to find the equilibrium position for a -1.0 nC charge. Let's assume this position is at a distance x from the first charge.
Using Coulomb's Law, we can set up the equation for the force between the charges as follows:
F = (k * (q1 * q3)) / (x^2)
Where q3 is the charge of -1.0 nC (which is equivalent to -1.0 × 10^-9 C).
Since the equilibrium position is the position where the net force on the -1.0 nC charge is zero, we can equate the forces between the charges:
(k * (q1 * q2)) / r^2 = (k * (q1 * q3)) / (x^2)
Plugging in the given values:
(8.98755 × 10^9 N · m^2/C^2 * (9.0 × 10^-9 C * 4.0 × 10^-9 C)) / (0.5 m^2) = (8.98755 × 10^9 N · m^2/C^2 * (9.0 × 10^-9 C * -1.0 × 10^-9 C)) / (x^2)
Simplifying the equation:
36.0 = -9.0 * (x^2)
Dividing both sides by -9.0:
-4.0 = x^2
Taking the square root of both sides:
x = ±2.0 cm
Since distance cannot be negative in this context, the equilibrium position for a -1.0 nC charge from the first charge is 2.0 cm.