Physics, 17.07.2020 19:01 mathmeup

Two small, identical conducting spheres repel each other with a force of 0.030 N when they are 0.65 m apart. After a conducting wire is connected between the spheres and then removed, they repel each other with a force of 0.075 N. What is the original charge on each sphere? (Enter the magnitudes in C.)

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Note that the methods applied in solving this question is the appropriate method. Check the parameters you gave in the question if you did not expect a complex number for the charges. Thanks

$q_1 = 0.00000119 + j0.00000145 C \\q_2 = 0.00000119 - j0.00000145 C$

Explanation:

Note: When a conducting wire was connected between the spheres, the same charge will flow through the two spheres.

The two charges were 0.65 m apart. i.e. d = 0.65 m

Force, F = 0.030 N

The force or repulsion between the two charges can be calculated using the formula:

$F = \frac{kq^2}{d^2} \\\\0.030 = \frac{9 * 10^9 * q^2}{0.65^2}\\\\q = 1.19 * 10^{-6} C$

Due to the wire connected between the two spheres, $q_1 = q_2 = 1.19 * 10^{-6} C$

The sum of the charges on the two spheres = $q_1 + q_2 = 2.38 * 10^{-6} C$

Note: When the conducting wire is removed, the two spheres will no longer contain similar charges but will rather share the total charge unequally

Let charge in the first sphere = q_1

Charge in the second sphere, q₂ = $2.38 * 10^{-6} - q_1$

Force, F = 0.075 N

$F = \frac{k q_1 q_2}{r^2} \\\\0.075 = \frac{9*10^9 * q_1 * (2.38*10^{-6} -q_1 )}{0.65^2}\\\\3.52 * 10^{-12} = q_1 * (2.38*10^{-6} -q_1 )\\\\3.52 * 10^{-12} = 2.38*10^{-6} q_1 - q_1^2\\\\q_1^2 - (2.38*10^{-6}) q_1 + (3.52 * 10^{-12}) = 0\\$

$q_1 = 0.00000119 + j0.00000145 C \\q_2 = 0.00000119 - j0.00000145 C$

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Answer from: Quest

Answer (d) the universe had cooled enough for atoms to combine, protons and neutrons were too far apart to form nuclei;

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Two small, identical conducting spheres repel each other with a force of 0.030 N when they are 0.65...