Particles of charge +65, +48, and −95 μC are placed in a line. The center one is L = 60cm from each of the others.Calculate the net force on the left charge due to the other two.
F = k Q1 Q2 /d^2
due to right one, +force because opposite sign
due to middle one, -force because of same sign
F = k(10^-6)(10^-6)(65) [ 95/1.2^2 -48/.6^2 ]
-46.9
To calculate the net force on the left charge due to the other two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is given by the equation:
F = k * (q1 * q2) / r^2
Where:
- F is the force between the charges
- k is the electrostatic constant (k = 9 × 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, we have three charges: +65 μC, +48 μC, and -95 μC. The left charge will experience forces due to the other two charges.
Let's calculate the net force on the left charge step-by-step:
Step 1: Calculate the force on the left charge due to the +65 μC charge.
Using Coulomb's Law:
F1 = k * (q1 * q2) / r^2
F1 = (9 × 10^9 Nm^2/C^2) * ((65 × 10^-6 C) * (q2)) / (60 cm)^2
Step 2: Calculate the force on the left charge due to the +48 μC charge.
Using Coulomb's Law:
F2 = k * (q1 * q2) / r^2
F2 = (9 × 10^9 Nm^2/C^2) * ((48 × 10^-6 C) * (q2)) / (60 cm)^2
Step 3: Calculate the net force on the left charge.
Since the third charge is -95 μC, it will exert a force in the opposite direction. So, we subtract the force created by it.
Net force = F1 + F2 - F3
F3 = (9 × 10^9 Nm^2/C^2) * ((95 × 10^-6 C) * (q2)) / (60 cm)^2
Net force = F1 + F2 - F3
By plugging in the values and performing the calculations, you should be able to find the net force on the left charge due to the other two charges.
To calculate the net force on the left charge due to the other two charges, we need to use Coulomb's Law, which states that the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = (k * |q₁ * q₂|) / r²
Where:
- F is the magnitude of the electrostatic force between the charges,
- k is the electrostatic constant and has a value of 9 * 10^9 N m²/C²,
- q₁ and q₂ are the charges of the two particles in question,
- r is the distance between the charges.
In this case, we have three charges. Let's identify them as follows:
q₁ = +65 μC
q₂ = +48 μC
q₃ = -95 μC
The center charge is L = 60 cm = 0.6 m away from each of the other charges.
First, let's calculate the force between the left charge and the center charge:
F₁₂ = (k * |q₁ * q₂|) / r₁₂²
Substituting the values:
F₁₂ = (9 * 10^9 N m²/C² * |65 μC * 48 μC|) / (0.6 m)²
Next, let's calculate the force between the left charge and the right charge:
F₁₃ = (k * |q₁ * q₃|) / r₁₃²
Substituting the values:
F₁₃ = (9 * 10^9 N m²/C² * |65 μC * (-95) μC|) / (0.6 m)²
Finally, we can calculate the net force on the left charge by summing up the forces:
Net Force = F₁₂ + F₁₃
After calculating the values for F₁₂ and F₁₃ and summing them up, you will get the net force on the left charge due to the other two charges.