1. If one point charge is located at each corners of a right triangle, where q1=q3= 5.0μC, q2= 2.0 μC, and a= 0.10 m. Find the resultant force felt by the third charge.
Well, aren't these charges just a bunch of corner buddies in a triangle! So, let's get down to business and find that resultant force, shall we?
First, we need to figure out the forces acting on the third charge. The force between two charges can be calculated using Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Now, let's label our points: q1 is at the right-angle, q2 is at the upper vertex, and q3 is at the lower vertex. We need to calculate the forces felt by q3 from q1 and q2, respectively.
Let's start with the force from q1 to q3. The charge of q1 is 5.0μC, so the force between q1 and q3 is given by:
F1-3 = (k * |5.0μC * 5.0μC|) / a^2
Next, let's move on to the force from q2 to q3. The charge of q2 is 2.0μC, so the force between q2 and q3 is given by:
F2-3 = (k * |2.0μC * 5.0μC|) / a^2
Now, since forces are vector quantities, we need to figure out the direction in which they act. For q3, the forces from q1 and q2 will be along the hypotenuse of the triangle.
To find the resultant force felt by the third charge, we need to calculate the net force experienced along the hypotenuse. We can use the Pythagorean theorem to do this:
Resultant force = sqrt(F1-3^2 + F2-3^2)
Just plug in the values we calculated earlier, and voila! You'll have your resultant force.
Now, I must warn you, the math might be a bit serious here, so be prepared to plot some charges and get your calculator ready!
To find the resultant force felt by the third charge, we need to calculate the force between each pair of charges and then use vector addition to find the net force.
Let's label the charges:
q1 = 5.0 μC
q2 = 2.0 μC
q3 = 5.0 μC
We'll use Coulomb's Law to calculate the force between each pair of charges:
The force between q1 and q3 is given by:
F13 = (k * |q1 * q3|) / r^2
Where:
k is the electrostatic constant, approximately equal to 9 × 10^9 N m^2/C^2
|q1 * q3| is the product of the magnitudes of charges |q1| and |q3|
r is the distance between the charges q1 and q3
The force between q2 and q3 is given by:
F23 = (k * |q2 * q3|) / r^2
Now, let's calculate the forces between each pair of charges:
F13 = (9 × 10^9 N m^2/C^2 * |5.0 μC * 5.0 μC|) / (0.1 m)^2
F13 = (9 × 10^9 N m^2/C^2 * 25 μC^2) / 0.01 m^2
F13 = (9 × 10^9 N m^2/C^2 * 25 × 10^-12 C^2) / 0.01 m^2
F13 = (225 × 10^-3 N) / 0.01 m^2
F13 = 22.5 N
F23 = (9 × 10^9 N m^2/C^2 * |2.0 μC * 5.0 μC|) / (0.1 m)^2
F23 = (9 × 10^9 N m^2/C^2 * 10 μC^2) / 0.01 m^2
F23 = (9 × 10^9 N m^2/C^2 * 10 × 10^-12 C^2) / 0.01 m^2
F23 = (90 × 10^-3 N) / 0.01 m^2
F23 = 9 N
Now, we have the forces acting on the third charge q3. To find the resultant force, we need to add these forces as vectors.
The force F13 acts along the hypotenuse of the right triangle, and the force F23 acts along one of the legs.
Using vector addition, we can find the net force:
Fnet = sqrt(F13^2 + F23^2)
Fnet = sqrt(22.5^2 + 9^2)
Fnet = sqrt(506.25 + 81)
Fnet = sqrt(587.25)
Fnet ≈ 24.21 N
Therefore, the resultant force felt by the third charge is approximately 24.21 N.
To find the resultant force felt by the third charge, you need to find the individual forces exerted on the third charge by the other two charges, and then add them together.
The formula to calculate the force between two point charges is given by Coulomb's Law:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the force between the charges
- k is the electrostatic constant (k = 9.0 x 10^9 Nm²/C²)
- |q1| and |q2| are the magnitudes of the charges
- r is the distance between the charges
Given that q1 = q3 = 5.0 μC, q2 = 2.0 μC, and a = 0.10 m, we can calculate the forces exerted on q3 by q1 and q2.
1. Force exerted by q1 on q3:
F1 = k * (|q1| * |q3|) / a^2
Substituting the given values:
F1 = (9.0 x 10^9 Nm²/C²) * (5.0 * 10^-6 C) * (5.0 * 10^-6 C) / (0.10 m)^2
2. Force exerted by q2 on q3:
F2 = k * (|q2| * |q3|) / a^2
Substituting the given values:
F2 = (9.0 x 10^9 Nm²/C²) * (2.0 * 10^-6 C) * (5.0 * 10^-6 C) / (0.10 m)^2
Now, we can calculate the resultant force by adding the forces F1 and F2:
Resultant Force = F1 + F2
Substitute the calculated values into the equation to find the resultant force.