Three positive particles of equal charge +11.o micro C, are located at the corners of an equilateral triangle of sides 15.0cm. Calculate magnitude and direction of the net force on each particle.
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thanks for your help ellie!
Yikes!
Sorry about the crazy response! It sure doesn't look like physics to me!
If you put each of the charges at the corners of equilateral triangles, then the angles are 60. Then, for each charge, you need to calculate the net electrical field that that charge feels. The sides are length r.
For example, consider triangle with q1 at lower left, q2 at top, and q3 at lower right.
the field felt by q1:
E net (x direction) = E2 (x direction) + E3 (x direction.
E net x = E2 cos60 + E3
= k/r^2 * q2cos60 + k/r^2 * q3
E net y = E2 (y direction + E3 (y direction)
E net y = E2 sin60 + 0
k/r^2 * q2sin60
Now you have the electrical field felt by q1.
To get the force, use F = qE
Hope this is a start for you!!
Why did the positive particles go to therapy?
Because they couldn't handle the negative charges in their lives!
But in all seriousness, to find the net force on each particle, you'll need to calculate the electric field due to the other two particles and then use the formula F = qE, where F is the force, q is the charge, and E is the electric field.
Let's consider one particle at a time:
Particle 1 (at the lower left corner):
To find the net force on particle 1, we need to calculate the electric field due to particles 2 and 3 separately:
Electric field due to particle 2:
E2 = k*q2/r^2, where k is Coulomb's constant, q2 is the charge of particle 2, and r is the distance between particle 1 and particle 2.
Electric field due to particle 3:
E3 = k*q3/r^2, where q3 is the charge of particle 3.
The net force on particle 1 is then given by:
F1 = q1*(E2 + E3)
Repeat this process for particles 2 and 3 to find the net forces on them.
Just a quick reminder, make sure to use the appropriate signs for the charges to determine the direction of the forces!
Keep calm and calculate on!
To calculate the net force on each particle using Coulomb's Law, you need to determine the electric field caused by the other two particles at the position of each particle.
Let's call the charges q1, q2, and q3, all equal to +11.0 μC, and the sides of the equilateral triangle length r = 15.0 cm.
For each charge, we'll calculate the net electric field in both the x and y directions using the formulas:
E_net_x = E2_x + E3_x
E_net_y = E2_y + E3_y
The electric field experienced by each charge due to the other charges can be calculated using the formula:
E = (k * q) / r^2
where k is the electrostatic constant and r is the distance between the charges.
Now, let's calculate the values step by step.
For q1 at the lower left corner:
E_net_x = (k * q2 * cos60) / r^2 + (k * q3) / r^2
E_net_y = (k * q2 * sin60) / r^2
For q2 at the top corner:
E_net_x = (-k * q1 * cos60) / r^2 + (k * q3 * cos60) / r^2
E_net_y = (-k * q1 * sin60) / r^2 + (k * q3 * sin60) / r^2
For q3 at the lower right corner:
E_net_x = (-k * q1) / r^2 + (-k * q2 * cos60) / r^2
E_net_y = (-k * q2 * sin60) / r^2
Finally, we can calculate the net force on each particle using the formula:
F = q * E_net
where F is the net force, q is the charge, and E_net is the net electric field in magnitude and direction.
Plug in the values of each charge, calculate the net electric field for each charge, and then multiply by the corresponding charge to obtain the net force for each particle.
Absolutely! Let me provide a step-by-step explanation on calculating the magnitude and direction of the net force on each particle.
1. Start by calculating the electric field due to each charge at the position of the other charges. The electric field is given by the formula E = k * q / r^2, where k is the electrostatic constant (9 x 10^9 N.m^2/C^2), q is the charge, and r is the distance between the charges.
2. Consider the first particle, q1. Calculate the electric field at its position due to q2 (E1 due to q2) and q3 (E1 due to q3) using the formula mentioned above.
3. Now, you need to decompose the electric field into its x and y components. The x-component of the electric field is given by E1x = E1 * cos(theta), where theta is the angle between the electric field and the x-axis. The y-component is given by E1y = E1 * sin(theta).
4. Repeat steps 2 and 3 for the other two particles (q2 and q3), calculating the electric fields at their positions due to the other charges and decomposing them into x and y components.
5. Once you have the x and y components of the electric fields for each particle, you can determine the net electric field by summing up the individual components. The net electric field components are obtained by adding the x-components together and adding the y-components together. Let's call the net electric field for q1 as Enet_x and Enet_y.
6. Now you can determine the magnitude and direction of the net force acting on each particle. The magnitude of the net force is given by F = q * E, where q is the charge and E is the net electric field. For each particle, substitute the appropriate charge and the calculated net electric field (magnitude) to determine the magnitude of the net force.
7. To find the direction of the net force, use the right-hand rule. The net force will act along the direction of the net electric field, which can be determined by summing up the x and y components. Use basic trigonometry to find the angle between the net electric field and the x-axis.
Repeat the steps above for each particle (q1, q2, and q3) to determine the magnitude and direction of the net force on each particle.
Remember to plug in the correct values into the equations, such as the charge of each particle and the distance between them (15.0 cm in this case).