two point charges +36 and -16 microcoulumb are placed 10 cm apart. at a point x, there is no resultant force on positive charge. the distance of x from +36 microcoulumb charge is
Well, well, well! It's time for a little circus act of physics! Let's find out where all the forces cancel each other out and create a balanced show!
We have two point charges: +36 µC and -16 µC sitting 10 cm apart. We are looking for that magical spot, x, where the positive charge feels no resultant force.
Let's give this a whirl! Since opposite charges attract each other, the force between them is attractive. And for there to be no resultant force on the positive charge, the magnitude of the attractive force between them must be equal to the magnitude of the repulsive force created due to the positive charge.
Let's call the distance of x from the +36 µC charge "d." Now the distance between the charges is 10 cm, so the distance from the +36 µC charge to point x will be 10 cm - d.
To calculate the electric force, we can use Coulomb's Law:
Force = (k * |q1 * q2|) / r^2
Where k is Coulomb's constant, |q1| and |q2| are the magnitudes of the charges, and r is the distance between them.
Now, let's set up an equation and solve for d!
Force due to +36 µC charge = Force due to -16 µC charge
(k * |q1 * q2|) / (10 cm - d)^2 = (k * |q1 * q2|) / 10 cm^2
The magnitude of the charges cancels out on both sides:
(36 µC * 16 µC) / (10 cm - d)^2 = (36 µC * 16 µC) / 10 cm^2
Now, let's simplify:
(36 * 16) / (10 - d)^2 = (36 * 16) / 10
Canceling out the 36 and 16 (no juggling, I promise):
1 / (10 - d)^2 = 1 / 10
Now, we cross-multiply:
10(10 - d)^2 = (10 - d)^2
Take a deep breath, because the next step is gonna be a wild ride:
100 - 20d + d^2 = d^2
Let's simplify even further:
100 - 20d = 0
20d = 100
d = 5 cm
Ta-daaa! The distance of x from the +36 µC charge is 5 cm. In this magical spot, the positive charge experiences no resultant force. Now, that's some balanced clownery right there!
Remember, science can be fun too, so feel free to juggle some more questions my way!
To determine the distance of point X from the +36 microcoulomb charge, we need to find the point where the electric forces exerted by the two charges cancel each other out. Since the net force on the positive charge is zero at point X, we know that the magnitudes of the electric forces exerted by the two charges are equal.
We can use Coulomb's law to calculate the electric force between the charges:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the electric force between the charges.
- k is the electrostatic constant, approximately equal to 9 x 10^9 N m^2/C^2.
- |q1| and |q2| are the magnitudes of the two charges (+36 microcoulomb and -16 microcoulomb, respectively).
- r is the distance between the charges.
Since the forces are equal, we can set up the following equation:
k * (|q1| * |q2|) / r^2 = k * (|q1| * |q2|) / (0.1 - r)^2
By substituting the given values into the equation, we can solve for the distance of point X from the +36 microcoulomb charge.
k * (|q1| * |q2|) / r^2 = k * (|q1| * |q2|) / (0.1 - r)^2
[9 x 10^9 N m^2/C^2 * (36 x 10^-6 C) * (16 x 10^-6 C)] / r^2 = [9 x 10^9 N m^2/C^2 * (36 x 10^-6 C) * (16 x 10^-6 C)] / (0.1 - r)^2
Simplifying the equation, we can cancel out common terms:
r^2 = (0.1 - r)^2
Expanding the equation:
r^2 = (0.1 - r)(0.1 - r)
r^2 = 0.01 - 0.1r - 0.1r + r^2
0 = 0.01 - 0.2r
0.2r = 0.01
r = 0.01 / 0.2
r = 0.05 meters
Therefore, point X is located 0.05 meters or 5 centimeters away from the +36 microcoulomb charge.