The test charge is 12 mm from Q1 and 20 mm from Q2. If Q1 has a relative charge of +4e and Q2 has a relative charge of +8e determine the magnitude and direction of the the result force acting on the test charge.
Use the formula ... F=1/4(PI) €¤ *Q1Q2/r^2 where r=12*10^-3.
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Answer
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Well, it seems like Q1 and Q2 are having a charged party! Let's see what happens.
First, we have to calculate the force between the test charge and Q1 using Coulomb's Law. Since Q1 has a relative charge of +4e, we substitute that value into the equation. Let's call this force F1.
F1 = (k * |Q1| * |test charge|) / r1^2
Where k is the electrostatic constant, |Q1| is the magnitude of Q1's charge, and r1 is the distance between the test charge and Q1.
Now, let's calculate the force between the test charge and Q2. Similar to Q1, we plug in the values. Let's call this force F2.
F2 = (k * |Q2| * |test charge|) / r2^2
Where |Q2| is the magnitude of Q2's charge, and r2 is the distance between the test charge and Q2.
Next, since the forces on the test charge are acting along the same line, we can find the net force by adding the vector sum of F1 and F2.
Resultant force = F1 + F2
Now, let's plug in the values and crunch some numbers to get the specific values for the force and its direction.
To determine the magnitude and direction of the resulting force acting on the test charge, we can use Coulomb's law. This law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:
F = k * |Q1 * Q2| / r^2
Where:
- F is the force between the charges,
- k is the Coulomb's constant (k = 9 x 10^9 N m^2/C^2),
- Q1 and Q2 are the respective charges of the two objects, and
- r is the distance between the charges.
In this case, we have two charges, Q1 and Q2, and we want to find the resulting force on the test charge. Let's calculate it step by step:
1. Calculate the force due to Q1:
- Q1 = +4e (relative charge of Q1)
- r1 = 12 mm = 0.012 m (distance from Q1 to the test charge)
- F1 = k * |Q1 * Q_test| / r1^2
2. Calculate the force due to Q2:
- Q2 = +8e (relative charge of Q2)
- r2 = 20 mm = 0.02 m (distance from Q2 to the test charge)
- F2 = k * |Q2 * Q_test| / r2^2
3. Calculate the resulting force:
- F_resultant = F1 + F2
4. Determine the magnitude and direction of the force:
- Magnitude: |F_resultant|
- Direction: This can be determined by the sign of the force. If the force is positive, it's repulsive, and if it's negative, it's attractive.
Note: The test charge, Q_test, is assumed to have a small magnitude compared to Q1 and Q2, so it does not significantly affect their forces on each other.
Now, you can substitute the values and calculate the magnitude and direction of the resulting force acting on the test charge.