Two +'ve charges separated by a distance 2m each other with a force of 0.36N. If the combined charge is 26mc , the charges are
To find the charges of the two positive charges, we can use Coulomb's Law which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
First, let's convert the force from Newtons to Coulombs since we are given the charges in milliCoulombs.
1 N = 1 kg.m/s²
1 C = 1 A.s
Given:
Force, F = 0.36 N
Combined charge, q = 26 mC = 26 × 10⁻³ C
Distance, r = 2 m
Now, let's rearrange Coulomb's Law to solve for the charges:
F = (k * |q₁ * q₂|) / r²
where k is the electrostatic constant (9 × 10⁹ N.m²/C²).
Plugging in the given values, we get:
0.36 N = (9 × 10⁹ N.m²/C² * |q₁ * q₂|) / (2 m)²
Now, rearranging the equation to solve for |q₁ * q₂|, we get:
|q₁ * q₂| = (0.36 N * 4 m²) / (9 × 10⁹ N.m²/C²)
|q₁ * q₂| = (1.44 N.m²) / (9 × 10⁹ N.m²/C²)
|q₁ * q₂| = 1.6 × 10⁻¹¹ C²
Since the charges are both positive, we can say:
q₁ * q₂ = 1.6 × 10⁻¹¹ C²
Given that the combined charge (q) is 26 mC = 26 × 10⁻³ C, and both charges are positive, we can set up the following equation:
q₁ + q₂ = 26 × 10⁻³ C
Now, we need to solve these two equations simultaneously to find q₁ and q₂.
Let's rewrite q₁ * q₂ = 1.6 × 10⁻¹¹ C² as:
q₁ = 1.6 × 10⁻¹¹ C² / q₂
Substituting this value of q₁ into the second equation:
(1.6 × 10⁻¹¹ C² / q₂) + q₂ = 26 × 10⁻³ C
Multiplying through by q₂:
1.6 × 10⁻¹¹ C² + q₂² = 26 × 10⁻³ C * q₂
Rearranging this equation:
q₂² - (26 × 10⁻³ C) * q₂ + 1.6 × 10⁻¹¹ C² = 0
Now, let's solve this quadratic equation. You can use the quadratic formula:
q₂ = (-b ± √(b² - 4ac)) / 2a
Here, a = 1, b = -(26 × 10⁻³ C), c = 1.6 × 10⁻¹¹ C²
Substituting these values into the formula, we get:
q₂ = (26 × 10⁻³ C ± √((26 × 10⁻³ C)² - 4(1)(1.6 × 10⁻¹¹ C²))) / (2(1))
Calculating this expression gives us two possible values for q₂. You can substitute each one back into the equation q₁ = 1.6 × 10⁻¹¹ C² / q₂ to find the corresponding q₁.
To determine the individual charges of the two positive charges, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is as follows:
F = k * (q1 * q2) / r^2
Where:
- F is the electric force between the charges
- k is Coulomb's constant (approximately 9 x 10^9 Nm^2/C^2)
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges
In this case, we are given the force F as 0.36 N and the distance r as 2 m. We are also told that the combined charge of the two charges is 26 mC (milliCoulombs), which is equivalent to 26 * 10^-3 C.
Substituting the given values into the formula, we have:
0.36 = (9 x 10^9) * (26 x 10^-3) * (26 x 10^-3) / (2^2)
Simplifying the equation:
0.36 = (9 x 10^9) * (26 x 10^-3)^2 / 4
0.36 = (9 x 10^9) * (26^2 x 10^-6) / 4
Now, multiply 26^2 by 10^-6:
0.36 = (9 x 10^9) * (676 x 10^-6) / 4
0.36 = (9 x 676) x (10^9 x 10^-6) / 4
0.36 = 6084 x (10^9 x 10^-6) / 4
Now, multiply 10^9 by 10^-6:
0.36 = 6084 x (10^9 x 10^-6) / 4
0.36 = 6084 x 10^3 / 4
0.36 = 15210 x 10^3 / 4
Now, divide by 4:
0.36 x 4 = 15210 x 10^3
1.44 = 15210 x 10^3
Now, divide by 15210:
1.44 / 15210 = 10^3
0.0000946919... = 10^3
Therefore, the individual charge of each positive charge is approximately 0.0000946919... C, or approximately 94.7 μC (microCoulombs).
Solve
F = k .q1q2 /2×2
0.36 = 9×10^9q1×q2/4
Q1×Q2= 1.6 /10^9 (1 st equation)
Q1+Q2 = 26×10^-6 (2nd equation )
So by solving this both equation u will get the answer !!!