Two positive point charges are placed on the x-axis. One, of magnitude 4Q, is placed at the origin. The other, of magnitude Q is placed at x=3 m. Neither charge is able to move. Where on the x-axis in meters can I place a third positive point charge such that the magnitude of the net force on the third charge is zero?
A 1.6-mole sample of an ideal gas is gently cooled at constant temperature 280 K. It contracts from initial volume 37 L to final volume V2. A total of 1.9 kJ of heat is removed from the gas during the contraction process. What is V2? Let the ideal-gas constant R = 8.314 J/(mol • K).
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A 1.6-mole sample of an ideal gas is gently cooled at constant temperature 280 K. It contracts from initial volume 37 L to final volume V2. A total of 1.9 kJ of heat is removed from the gas during the contraction process. What is V2? Let the ideal-gas constant R = 8.314 J/(mol • K).
To find the position on the x-axis where you can place a third positive point charge so that the net force on it is zero, you need to consider the forces exerted by the two existing charges.
Let's call the magnitude of the first charge placed at the origin "4Q" and the magnitude of the second charge placed at x=3m "Q". The net force on the third charge will be zero when the electrical forces exerted by the two charges on the third charge balance each other out.
The electrical force between two point charges can be calculated using Coulomb's Law:
F = k * (q1 * q2) / r^2
Where:
F is the magnitude of the electrical 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
For the third charge to experience a net force of zero, the magnitudes of the forces exerted by the two existing charges on the third charge should be equal in magnitude and opposite in direction.
Let's assume the magnitude of the third charge to be "q3".
So, we can equate the forces exerted by the two existing charges on the third charge:
F1 = F2
k * (4Q * q3) / r1^2 = k * (Q * q3) / r2^2
Simplifying the equation, we get:
(4Q) / r1^2 = Q / r2^2
Now, substitute the given values:
r1 = distance between the first charge (at origin) and the third charge (unknown)
r2 = distance between the second charge (at x=3m) and the third charge (unknown)
(4Q) / r1^2 = Q / r2^2
Cancel the charges (Q) on both sides:
4 / r1^2 = 1 / r2^2
Rearrange the equation:
r1^2 = 4 * r2^2
Taking the square root of both sides:
r1 = 2 * r2
Since the distance between the second charge and the third charge is greater than the distance between the first charge and the third charge, we can assume r1 > r2.
Thus, the ratio between r1 and r2 is 2:1.
Therefore, to find the position where the net force on the third charge is zero, we need to divide the distance between the two existing charges (from x=0 to x=3m) in the ratio of 2:1.
The total distance between the two charges is 3m (x=3m - x=0). So, we divide this distance in the ratio of 2:1:
r1 = 2/3 * (x=3m - x=0) = 2m
The position on the x-axis where you can place the third positive point charge so that the net force on it is zero is at 2 meters.