I need a answer about these? Calculate the net electric force exerted on a particle of charge -4.0mc due to the influence of charge +5.0mc and -3.0mc at distance of 20cm & 80cm, 50cm from it?
To calculate the net electric force exerted on a particle, we need to calculate the individual forces due to each charge and then add them together. The formula to calculate the electric force is given by Coulomb's Law:
F = k * |q1 * q2| / r^2
Where:
F is the electric force
k is Coulomb's constant (9.0 x 10^9 Nm^2/C^2)
q1 and q2 are the charges of the two particles
r is the distance between the particles
Let's calculate the electric forces due to each charge individually:
1. Positive charge of +5.0 mc at a distance of 20 cm:
F1 = (9.0 x 10^9 Nm^2/C^2) * |(-4.0 mc) * (+5.0 mc)| / (0.2 m)^2
2. Negative charge of -3.0 mc at a distance of 20 cm:
F2 = (9.0 x 10^9 Nm^2/C^2) * |(-4.0 mc) * (-3.0 mc)| / (0.2 m)^2
3. Negative charge of -3.0 mc at a distance of 80 cm:
F3 = (9.0 x 10^9 Nm^2/C^2) * |(-4.0 mc) * (-3.0 mc)| / (0.8 m)^2
4. Positive charge of +5.0 mc at a distance of 50 cm:
F4 = (9.0 x 10^9 Nm^2/C^2) * |(-4.0 mc) * (+5.0 mc)| / (0.5 m)^2
Now, let's plug in the values and calculate the forces:
1. F1 = (9.0 x 10^9 Nm^2/C^2) * |(-4.0 mc) * (+5.0 mc)| / (0.2 m)^2
= (9.0 x 10^9 Nm^2/C^2) * (20 x 10^-6 C) / (0.04 m)^2
= (9.0 x 10^9 Nm^2/C^2) * (20 x 10^-6 C) / 0.0016 m^2
= 1125 N
2. F2 = (9.0 x 10^9 Nm^2/C^2) * |(-4.0 mc) * (-3.0 mc)| / (0.2 m)^2
= (9.0 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) / (0.04 m)^2
= (9.0 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) / 0.0016 m^2
= 675 N
3. F3 = (9.0 x 10^9 Nm^2/C^2) * |(-4.0 mc) * (-3.0 mc)| / (0.8 m)^2
= (9.0 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) / (0.8 m)^2
= (9.0 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) / 0.64 m^2
= 281.25 N
4. F4 = (9.0 x 10^9 Nm^2/C^2) * |(-4.0 mc) * (+5.0 mc)| / (0.5 m)^2
= (9.0 x 10^9 Nm^2/C^2) * (20 x 10^-6 C) / (0.5 m)^2
= (9.0 x 10^9 Nm^2/C^2) * (20 x 10^-6 C) / 0.25 m^2
= 720 N
Finally, to calculate the net electric force, we need to add up all the forces:
Net Force = F1 + F2 + F3 + F4
= 1125 N + 675 N + 281.25 N + 720 N
= 2801.25 N
Therefore, the net electric force exerted on the particle is 2801.25 N.
To calculate the net electric force exerted on a particle, you need to use Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for calculating the electric force between two charges is:
F = k * (|Q1| * |Q2|) / r^2
Where:
- F is the electric force
- k is the electrostatic constant equal to 8.99 × 10^9 N m^2/C^2
- |Q1| and |Q2| are the magnitudes of the two charges
- r is the distance between the charges
Let's calculate the net electric force using the given values:
Charge 1: Q1 = -4.0 mc (microcoulombs)
Charge 2: Q2 = +5.0 mc (microcoulombs)
Charge 3: Q3 = -3.0 mc (microcoulombs)
Distance 1: r1 = 20 cm = 0.20 m
Distance 2: r2 = 80 cm = 0.80 m
Distance 3: r3 = 50 cm = 0.50 m
First, calculate the force due to Charge 2 at a distance of 20 cm:
F1 = k * (|Q1| * |Q2|) / r1^2
Substituting the values:
F1 = (8.99 × 10^9 N m^2/C^2) * (4.0 × 10^-6 C) * (5.0 × 10^-6 C) / (0.20 m)^2
Now, calculate the force due to Charge 3 at a distance of 20 cm:
F2 = k * (|Q1| * |Q3|) / r1^2
Substituting the values:
F2 = (8.99 × 10^9 N m^2/C^2) * (4.0 × 10^-6 C) * (3.0 × 10^-6 C) / (0.20 m)^2
Next, calculate the force due to Charge 2 at a distance of 80 cm:
F3 = k * (|Q1| * |Q2|) / r2^2
Substituting the values:
F3 = (8.99 × 10^9 N m^2/C^2) * (4.0 × 10^-6 C) * (5.0 × 10^-6 C) / (0.80 m)^2
Finally, calculate the force due to Charge 3 at a distance of 50 cm:
F4 = k * (|Q1| * |Q3|) / r3^2
Substituting the values:
F4 = (8.99 × 10^9 N m^2/C^2) * (4.0 × 10^-6 C) * (3.0 × 10^-6 C) / (0.50 m)^2
To find the net electric force, add the forces together:
Net electric force = F1 + F2 + F3 + F4
Calculate the values of F1, F2, F3, F4 using the formulas, substitute the values, and then add them together to find the net electric force.