three point charges are located at the corners of a right triangle where q1=q3= 5uC,Q2= -2uC and r =10cm.(angle q1 q2q3=90 and
and something else. What you need to do is figure each of the forces in x,y components, then add them as vectors.
To find the net electric field at a point, we need to calculate the contribution from each charge and then add up the vector components of these contributions.
Given:
q1 = q3 = 5 μC
q2 = -2 μC
r = 10 cm
We can use Coulomb's law to find the magnitude of the electric field due to each charge:
1. E1 = k * |q1| / r1^2
Considering q1 at corner q1 and the point of interest as the reference point, r1 = r * √2
2. E2 = k * |q2| / r2^2
Considering q2 at corner q2 and the point of interest as the reference point, r2 = r
3. E3 = k * |q3| / r3^2
Considering q3 at corner q3 and the point of interest as the reference point, r3 = r
Since the triangle is a right triangle, the angles are as follows:
angle q1-q2-q3 = 90 degrees (right angle)
Next, we calculate the vector components of each electric field:
1. E1x = E1 * cos(angle1)
E1y = E1 * sin(angle1)
Since angle1 = 45 degrees, cos(angle1) = sin(angle1) = 1/√2
2. E2x = E2 * cos(angle2)
E2y = E2 * sin(angle2)
Since angle2 = 0 degrees, cos(angle2) = 1 and sin(angle2) = 0
3. E3x = E3 * cos(angle3)
E3y = E3 * sin(angle3)
Since angle3 = 90 degrees, cos(angle3) = 0 and sin(angle3) = 1
Finally, we can find the net electric field by adding up the vector components:
Net Ex = E1x + E2x + E3x
Net Ey = E1y + E2y + E3y
Let's calculate the values step-by-step:
Using Coulomb's law:
k = 9 * 10^9 Nm^2/C^2
1. Magnitude of electric field due to q1:
E1 = (9 * 10^9 Nm^2/C^2) * (5 * 10^-6 C) / [(10 cm * √2)^2]
= (9 * 10^9 * 5 * 10^-6) / (100 * 2)
= (45 * 10^3) / 200
= 225 / 200
= 1.125 * 10^3 N/C
2. Magnitude of electric field due to q2:
E2 = (9 * 10^9 Nm^2/C^2) * (2 * 10^-6 C) / (10 cm)^2
= (9 * 10^9 * 2 * 10^-6) / 100
= (18 * 10^3) / 100
= 180 / 100
= 1.8 * 10^3 N/C
3. Magnitude of electric field due to q3:
E3 = (9 * 10^9 Nm^2/C^2) * (5 * 10^-6 C) / (10 cm)^2
= (9 * 10^9 * 5 * 10^-6) / 100
= (45 * 10^3) / 100
= 450 / 100
= 4.5 * 10^3 N/C
Next, let's calculate the vector components:
1. Ex1 = E1 * cos(45 degrees)
= (1.125 * 10^3 N/C) * (1/√2)
= 1.125 * 10^3 / √2 N/C
Ey1 = E1 * sin(45 degrees)
= (1.125 * 10^3 N/C) * (1/√2)
= 1.125 * 10^3 / √2 N/C
2. Ex2 = E2 * cos(0 degrees)
= (1.8 * 10^3 N/C) * 1
= 1.8 * 10^3 N/C
Ey2 = E2 * sin(0 degrees)
= (1.8 * 10^3 N/C) * 0
= 0 N/C
3. Ex3 = E3 * cos(90 degrees)
= (4.5 * 10^3 N/C) * 0
= 0 N/C
Ey3 = E3 * sin(90 degrees)
= (4.5 * 10^3 N/C) * 1
= 4.5 * 10^3 N/C
Finally, let's calculate the net electric field components:
Net Ex = Ex1 + Ex2 + Ex3
= (1.125 * 10^3) / √2 + 1.8 * 10^3 + 0
= 1.125 * 10^3 / √2 + 1.8 * 10^3
≈ 1792.89 N/C
Net Ey = Ey1 + Ey2 + Ey3
= (1.125 * 10^3) / √2 + 0 + 4.5 * 10^3
= 1.125 * 10^3 / √2 + 4.5 * 10^3
≈ 4655.86 N/C
Therefore, the net electric field at the point of interest is approximately 1792.89 N/C in the x-direction and 4655.86 N/C in the y-direction.
To find the net electrostatic force on charge q1 due to the other two charges, we can use Coulomb's Law:
F = k * (|q1| * |q2| / r^2)
Where:
F is the electrostatic force between the charges,
k is the electrostatic constant (= 9 * 10^9 Nm^2/C^2),
|q1| and |q2| are the magnitudes of the charges q1 and q2, and
r is the distance between the charges.
In this case, we have three charges arranged in a right triangle. Let's label them as follows:
q1 is at the right angle.
q2 is at one of the acute angles.
q3 is at the remaining acute angle.
Given:
q1 = q3 = 5 μC (microcoulombs)
q2 = -2 μC (microcoulombs)
r = 10 cm = 0.10 m
We need to find the net electrostatic force on q1 due to q2 and q3.
Since q1 is at the right angle, it does not have any electrostatic force acting on it from q2. However, both q2 and q3 will exert forces on q1.
We can find the net force by calculating the individual forces and adding them together:
Step 1: Calculate the force on q1 due to q2.
F1 = k * (|q1| * |q2| / r^2)
Substituting the values:
F1 = (9 * 10^9 Nm^2/C^2) * (5 * 10^-6 C * 2 * 10^-6 C) / (0.10 m)^2
Step 2: Calculate the force on q1 due to q3.
F2 = k * (|q1| * |q3| / r^2)
Substituting the values:
F2 = (9 * 10^9 Nm^2/C^2) * (5 * 10^-6 C * 5 * 10^-6 C) / (0.10 m)^2
Step 3: Calculate the net force on q1.
Net Force = F1 + F2
Simplifying the equations and performing the calculations will give you the final answer.