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

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

1 answer

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

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

where \( k \) is Coulomb's constant.

Let's evaluate the options:

  1. An object with a +3 charge at a distance of 5 cm: \[ F = k \frac{|-3 \cdot 3|}{(0.05)^2} = k \frac{9}{0.0025} = k \cdot 3600 \]

  2. An object with a +3 charge at a distance of 2 cm: \[ F = k \frac{|-3 \cdot 3|}{(0.02)^2} = k \frac{9}{0.0004} = k \cdot 22500 \]

  3. An object with a -4 charge at a distance of 2 cm: \[ F = k \frac{|-3 \cdot -4|}{(0.02)^2} = k \frac{12}{0.0004} = k \cdot 30000 \]

  4. An object with a -3 charge at a distance of 5 cm: \[ F = k \frac{|-3 \cdot -3|}{(0.05)^2} = k \frac{9}{0.0025} = k \cdot 3600 \]

Now we summarize the forces calculated:

  1. +3 charge, 5 cm: \( k \cdot 3600 \)
  2. +3 charge, 2 cm: \( k \cdot 22500 \)
  3. -4 charge, 2 cm: \( k \cdot 30000 \)
  4. -3 charge, 5 cm: \( k \cdot 3600 \)

The strongest attraction occurs for the third option: An object with a -4 charge at a distance of 2 cm which results in a force of \( k \cdot 30000 \).

Thus, the answer is: An object with a -4 charge at a distance of 2 cm.