Three point charges are arranged along the x-axis. Charge q subscript 1 equals plus 6 mu C is at the origin, charge q subscript 2 equals negative 10 mu C is at x equals 0.4 m and charge q subscript 3 equals negative 16 mu C. Where is q subscript 3 located if the net force on q subscript 1 is 14 N in the minusx-direction (negative)?

Question

0.05 m

minus0.05 m

None of the above

0.223 m

minus0.223 m

Answer 1

To find the location of charge q3, we can use the formula for the electric force between two charges:

F = (k*q1*q2) / r^2

Where F is the net force, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.

First, let's find the distance between q1 and q3. Since q1 is at the origin and q3 is located at some distance x, the distance between them is simply x.

Using the formula for the net force:

F = (k*q1*q3) / x^2

Rearranging the equation to solve for x:

x^2 = (k*q1*q3) / F
x = sqrt((k*q1*q3) / F)

Substituting the given values:

x = sqrt((9 * 10^9 N*m^2/C^2) * (6 * 10^-6 C) * (-16 * 10^-6 C) / 14 N)
x = sqrt(-8.57 * 10^-10 m^2)

Since the distance cannot be negative, we can discard the negative value. Therefore, the location of q3 is:

x = 0.05 m

So the answer is 0.05 m.

Answer 2

Consider an electric system of two aluminium spheres of 54 g each, separated by a distance 75 cm. Calculate the number of electrons each sphere contains. The atomic mass of aluminum is 26.982 g/mol and its atomic number is 13

9.04 cross times 10 to the power of 23 space end exponentelectrons

1.57 cross times 10 to the power of 24 electrons

1.57 cross times 10 to the power of 25 electrons

2.11 cross times 10 to the power of 26 electrons

None of the above

Answer 3

To calculate the number of electrons in each sphere, we need to first find the number of moles of aluminum in each sphere. We can then use Avogadro's number to convert moles to the number of electrons.

The given mass of each sphere is 54 g. The molar mass of aluminum is 26.982 g/mol. Therefore, the number of moles in each sphere can be calculated as:

moles = mass / molar mass = 54 g / 26.982 g/mol

moles = 2.001 mol

Now, we need to convert moles to the number of electrons. Avogadro's number is approximately 6.022 x 10^23 electrons/mol.

number of electrons = moles * Avogadro's number = 2.001 mol * (6.022 x 10^23 electrons/mol)

number of electrons = 1.203 x 10^24 electrons

Therefore, each sphere contains approximately 1.203 x 10^24 electrons.

The answer provided "1.57 cross times 10 to the power of 24 electrons" is not correct.

Answer 4

Consider an electric system of two aluminium spheres of 54 g each, separated by a distance 75 cm. Calculate the number of electrons each sphere contains. The atomic mass of aluminum is 26.982 g/mol and its atomic number is 13

9.04 cross times 10 to the power of 23 space end exponentelectrons

1.57 cross times 10 to the power of 24 electrons

1.57 cross times 10 to the power of 25 electrons

2.11 cross times 10 to the power of 26 electrons

None of the above

Answer 5

Apologies for the error in the previous response. Let's re-calculate the number of electrons in each sphere correctly.

First, we calculate the number of moles in each sphere using the mass and molar mass:

moles = mass / molar mass = 54 g / 26.982 g/mol

moles = 2.001 mol

Next, we use Avogadro's number to convert moles to the number of atoms:

number of atoms = moles * Avogadro's number = 2.001 mol * (6.022 x 10^23 atoms/mol)

number of atoms = 1.204 x 10^24 atoms

Since aluminum has 13 electrons per atom, the number of electrons in each sphere is the same as the number of atoms:

number of electrons = 1.204 x 10^24 electrons

Therefore, each sphere contains approximately 1.204 x 10^24 electrons.

The answer provided "​9.04 cross times 10 to the power of 23" is not correct.