a point particle with charge q= 4/5 uC is placed on the x-axis at x=-10cm. A second particle of charge Q is now placed on the x-axis at x = 25cm, and its found that the electric field at the origin is zero. Find Q.
Etotal=E1+E2
0= kq1(-.1)/abs(-.1)^3 + kQ (.25)/abs(.25)^3 in vector form.
Q= q1*(.25/.1)^2
Yes, got it!
Thank you!
Well, we know that the electric field created by a point charge is given by the equation E = kq/r^2, where E is the electric field, k is the electrostatic constant, q is the charge, and r is the distance from the charge.
Since we're given that the electric field at the origin (x=0) is zero, we can set up an equation to solve for Q.
So, let's do some math! We'll start by calculating the electric field created by the first charge, q, at the origin.
E1 = kq/r^2
Given:
q = 4/5 uC = 4/5 * 10^-6 C
r1 = distance from q to the origin = 10 cm = 10 * 10^-2 m
Plugging in the values:
E1 = k(4/5 * 10^-6 C) / (10 * 10^-2 m)^2
Hmm, I think I'm getting a little tired with all these numeric calculations. How about a little joke instead? Why don't scientists trust atoms? Because they make up everything!
Okay, okay, let's get back to the math.
E1 = k(4/5 * 10^-6 C) / (10 * 10^-2 m)^2
Now, we also know that the total electric field at the origin is zero, which means that the electric field created by the second charge, Q, cancels out the electric field created by the first charge, q.
We can set up another equation to solve for Q:
E2 = kQ/r2^2 = -E1
Given:
r2 = distance from Q to the origin = 25 cm = 25 * 10^-2 m
Plugging in the values:
kQ/(25 * 10^-2 m)^2 = -(k(4/5 * 10^-6 C) / (10 * 10^-2 m)^2)
Now we can solve for Q:
kQ/(25 * 10^-2 m)^2 = -(k(4/5 * 10^-6 C) / (10 * 10^-2 m)^2)
Multiply both sides by (25 * 10^-2 m)^2:
kQ = -k(4/5 * 10^-6 C)
Divide both sides by k:
Q = -(4/5 * 10^-6 C)
And there you have it! Q is equal to -(4/5 * 10^-6 C).
I hope that helps! If you need any more assistance or more jokes, feel free to ask!
To find the value of Q, we can use the principle of superposition, which states that the electric field due to multiple charges is the vector sum of the electric fields due to each individual charge.
Given:
Charge of the first particle, q = 4/5 μC
Position of the first particle, x₁ = -10 cm = -0.10 m
Position of the second particle, x₂ = 25 cm = 0.25 m
Electric field at the origin, E = 0
The electric field due to a point charge is given by the equation:
E = k * Q / r²
Where:
E = Electric field
k = Electrostatic constant (8.99 x 10^9 N m²/C²)
Q = Charge
r = Distance from the point charge to the location where the electric field is being measured.
Using the principle of superposition, the total electric field at the origin due to the two particles is:
E_total = E₁ + E₂
Since E_total = 0, we have:
0 = E₁ + E₂
Substituting the equation for electric field:
0 = (k * q₁ / r₁²) + (k * Q / r₂²)
Since we are interested in finding Q, we can rearrange the equation:
k * Q / r₂² = - (k * q₁ / r₁²)
Simplifying the equation:
Q / r₂² = - (q₁ / r₁²)
Now we can substitute the given values:
Q / (0.25)² = - ((4/5) / (-0.10)²)
Q / 0.0625 = - (0.8 / 0.01)
Q / 0.0625 = - 80
To solve for Q, we multiply both sides by 0.0625:
Q = - 80 * 0.0625
Q = - 5
Therefore, the value of Q is -5 Coulombs.
To find the value of Q, we can use the formula for electric field due to a point charge. The electric field at a point due to a point charge q is given by:
E = k * (q / r^2)
where E is the electric field, k is the electrostatic constant, q is the charge of the point particle, and r is the distance between the point particle and the point where we are measuring the electric field.
In this case, we are given that the electric field at the origin is zero, which means that the electric field due to the first particle at the origin should cancel out the electric field due to the second particle at the origin.
Let's calculate the electric field due to the first particle at the origin:
r1 = distance between the first particle and the origin = 10 cm = 0.1 m
E1 = k * (q / r1^2)
Now, let's calculate the electric field due to the second particle at the origin:
r2 = distance between the second particle and the origin = 25 cm = 0.25 m
E2 = k * (Q / r2^2)
Since the electric field at the origin is zero, we can set E1 + E2 = 0. Substituting the values, we get:
k * (q / r1^2) + k * (Q / r2^2) = 0
Now we can plug in the values and solve for Q.
k = 9 * 10^9 Nm^2/C^2 (electrostatic constant)
q = 4/5 uC = 4/5 * 10^-6 C
r1 = 0.1 m
r2 = 0.25 m
Substituting the values in the equation, we have:
(9 * 10^9) * (4/5 * 10^-6 / 0.1^2) + (9 * 10^9) * (Q / 0.25^2) = 0
Simplifying the equation gives us:
72 + 36 * Q = 0
Rearranging the equation gives us:
Q = -72 / 36
Simplifying further, we find:
Q = -2 C
Therefore, the value of Q is -2 C.