A balloon rubbed against a pair of jeans gains a charge of -6x10^-6 C. If the balloon is moved to a distance of 0.25 m away from the jeans, what is the size and direction of the electric force between the balloon and jeans ?
Well, looks like someone wants to get to the bottom of this electric situation! Let's dive in, shall we?
First off, with a charge of -6x10^-6 C, that balloon got more shocks than a comedian on stage! Now, let's calculate the electric force between the balloon and jeans.
The electric force between two charges is given by Coulomb's Law, which states:
F = (k * |Q1 * Q2|) / r^2
Where F is the electric force, k is the electrostatic constant, Q1 and Q2 are the charges, and r is the distance between them.
Since the balloon has a charge of -6x10^-6 C, and the jeans have an equal and opposite charge, we can say that Q1 = -6x10^-6 C and Q2 = 6x10^-6 C.
Now, the distance between them is 0.25 m, which we'll plug in as r = 0.25 m.
Using the values and plugging them into the formula, we end up with:
F = (9x10^9 * |-6x10^-6 * 6x10^-6|) / (0.25)^2
Calculating that would be like trying to juggle flaming torches while riding a unicycle, so let's just punch it into a calculator instead:
F ≈ -5.76 x 10^-4 Newtons
So, the size of the electric force is approximately -5.76 x 10^-4 Newtons. The negative sign tells us it's an attractive force because opposite charges attract. But hey, don't worry about the direction; we'll leave that one hanging in the air for now!
Remember, though, this answer is electrifyingly humorous, not scientifically accurate. So, take it with a grain of salt or a spark of laughter!
To find the electric force between the balloon and jeans, we can use Coulomb's Law, which states that the electric force between two charged objects is given by:
F = (k * |q1 * q2|) / r^2
Where:
F is the electric force
k is the electrostatic constant (9 x 10^9 N * m^2 / C^2)
|q1| and |q2| are the magnitudes of the charges
r is the distance between the charges
Given:
Charge on the balloon, q1 = -6 x 10^-6 C (negative charge)
Distance between the balloon and jeans, r = 0.25 m
Charge on the jeans, q2 = unknown (to be determined)
Since the charge on the balloon is negative, the charge on the jeans must be positive to make the force attractive. Let's solve for the charge on the jeans, q2:
F = (k * |q1 * q2|) / r^2
Rearranging the formula, we have:
|q2| = (F * r^2) / (k * |q1|)
Plugging in the given values:
|q2| = (F * (0.25)^2) / (9 x 10^9 * 6 x 10^-6)
Now, let's calculate |q2|:
|q2| = F * (0.25)^2 / 54 x 10^3
|q2| = F * (0.625 * 10^-2) / 54 x 10^3
|q2| = (0.625 F) / (54 x 10^3) * 10^-2
Now, substitute the value of F = -6 x 10^-6 C:
|q2| = (0.625 * (-6 x 10^-6)) / (54 x 10^3) * 10^-2
|q2| = (-3.75 x 10^-6) / (54 x 10^3) * 10^-2
|q2| = (-3.75 / (54 x 10^3)) x 10^-8
|q2| ≈ -0.694 x 10^-8 C
Since the magnitude of the charge is positive, we take the positive value:
q2 ≈ 0.694 x 10^-8 C
Therefore, the size of the electric force between the balloon and jeans is given by Coulomb's Law, and the direction of the force is attractive.
To find the electric force between the balloon and jeans, first, we need to know the value of the electrostatic force constant, represented by k.
The equation for electric force is given by Coulomb's law:
F = k * (q1 * q2) / r^2
Where:
F is the electric force
k is the electrostatic force constant (approximately 8.99 x 10^9 N m^2/C^2)
q1 and q2 are the charges of the objects
r is the distance between the objects
In this case, the charge of the balloon is -6 x 10^-6 C, and the distance between the balloon and jeans is 0.25 m. The charge of the jeans is not provided, so we'll assume it to be an equal and opposite charge (+6 x 10^-6 C) to the balloon's charge.
Using Coulomb's law, we can calculate the electric force:
F = (8.99 x 10^9 N m^2/C^2) * (-6 x 10^-6 C) * (6 x 10^-6 C) / (0.25 m)^2
Now, let's calculate:
F = (8.99 x 10^9) * (-6 x 10^-6) * (6 x 10^-6) / (0.25)^2
F = -0.8624 N
Hence, the size of the electric force between the balloon and jeans is approximately 0.8624 N. The negative sign indicates that the force is attractive since the charges are opposite in sign.
Therefore, the size of the electric force is 0.8624 N, and the direction is attractive towards each other.