A positive and a negative charge are positioned as shown:
+
|
- _______|
The distance from - to corner is 4.00m and the distance from corner to + is 3.00m.
Q1 = 4.00 microCoulomb
Q2 = -4.00 microCoulomb
1. What is the distance between the charges?
2. What is the angle of West of south?
3. What is the force of + on -?
4. What is the force of - on +?
To answer these questions, we can use Coulomb's Law which states that the electric force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
1. The distance between the charges can be calculated using the Pythagorean theorem since we have a right triangle formed by the two sides and the hypotenuse. The distance from - to the corner is 4.00m and the distance from the corner to + is 3.00m. Using the Pythagorean theorem (a² + b² = c²), we can find the distance between the charges (c):
c² = (4.00m)² + (3.00m)²
c² = 16.00m² + 9.00m²
c² = 25.00m²
c = √25.00m²
c = 5.00m
Therefore, the distance between the charges is 5.00m.
2. To find the angle of West of south (θ), we can use trigonometry. Since we have a right triangle, we can use the tangent function:
tan(θ) = Opposite side / Adjacent side
In this case, the opposite side is 3.00m (measured west) and the adjacent side is 4.00m (measured south). Therefore:
tan(θ) = 3.00m / 4.00m
θ = tan^(-1)(3.00m / 4.00m)
Using a calculator, we find θ ≈ 36.87° (rounded to two decimal places).
Therefore, the angle of West of south is approximately 36.87°.
3. To calculate the force of + on -, we can use Coulomb's Law. The formula is:
F = (k * |Q1 * Q2|) / r²
Where:
F is the force between the charges,
k is Coulomb's constant (8.99 x 10^9 N m²/C²),
Q1 and Q2 are the magnitudes of the charges, and
r is the distance between the charges.
Plugging in the values:
F = (8.99 x 10^9 N m²/C²) * |(4.00 x 10^-6 C) * (-4.00 x 10^-6 C)| / (5.00m)²
F = 8.99 x 10^9 N m²/C² * 16.00 x 10^-12 C² / 25.00m²
F = 0.57504 N
Therefore, the force of + on - is approximately 0.57504 Newtons.
4. The force of - on + will have the same magnitude as the force of + on -, but in the opposite direction due to the opposite sign of the charges. Therefore, the force of - on + is also approximately 0.57504 Newtons, but directed in the opposite direction.
Therefore, the force of - on + is approximately -0.57504 Newtons.