A student has an object with a charge of -3 Coulombs. Which of the following objects would have the strongest attraction to object A?(1 point)

Responses

An object with a -4 charge at a distance of 2 cm
An object with a -4 charge at a distance of 2 cm

An object with a +3 charge at a distance of 2 cm
An object with a +3 charge at a distance of 2 cm

An object with a -3 charge at a distance of 5 cm
An object with a -3 charge at a distance of 5 cm

An object with a +3 charge at a distance of 5 cm

1 answer

To determine which object has the strongest attraction to the charged object A (with a charge of -3 Coulombs), we can use Coulomb's law, which states that the force \( F \) between two charges \( q_1 \) and \( q_2 \) is given by the formula:

\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]

where:

  • \( k \) is Coulomb's constant,
  • \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and
  • \( r \) is the distance between the charges.

Given that the most attractive force occurs between opposite charges, we identify that the object with a positive charge will attract the negative charge of object A.

Now, we will compare the provided options:

  1. An object with a charge of -4 at a distance of 2 cm:

    • \( F = k \frac{|-3 \cdot -4|}{(0.02)^2} = k \frac{12}{0.0004} \) (repulsive, not attractive)
  2. An object with a charge of +3 at a distance of 2 cm:

    • \( F = k \frac{|-3 \cdot +3|}{(0.02)^2} = k \frac{9}{(0.02)^2} = k \frac{9}{0.0004} \)
  3. An object with a charge of -3 at a distance of 5 cm:

    • \( F = k \frac{|-3 \cdot -3|}{(0.05)^2} = k \frac{9}{(0.05)^2} = k \frac{9}{0.0025} \) (repulsive, not attractive)
  4. An object with a charge of +3 at a distance of 5 cm:

    • \( F = k \frac{|-3 \cdot +3|}{(0.05)^2} = k \frac{9}{(0.05)^2} = k \frac{9}{0.0025} \)

Now we calculate the magnitudes of the attractive forces:

  • For the +3 charge at 2 cm: \[ F = k \frac{9}{0.0004} = 22500 k \]

  • For the +3 charge at 5 cm: \[ F = k \frac{9}{0.0025} = 3600 k \]

Comparing these values, the charge of +3 at a distance of 2 cm produces a much stronger attractive force (22500 k) compared to the charge of +3 at a distance of 5 cm (3600 k).

Thus, the object with the strongest attraction to the object with a charge of -3 Coulombs is:

An object with a +3 charge at a distance of 2 cm.