Two charges of # 6 C # and # -3 C# are positioned on a line at points # -7 # and # 5 #, respectively. What is the net force on a charge of # -3 C# at # 2 #?

Question

Two charges of #  6  C # and #  -3   C# are positioned on a line at points # -7  # and # 5  #, respectively.  What is the net force on a charge of #  -3  C# at #  2  #?

Charlotte Aaron · Accepted Answer

The net force is #=9*10^9N#

Between the charges, the net force is

#F=k(Q_1Q_3)/r_1^2+k(Q_2Q_3)/r_2^2#

Where #r# is the distance between the charges

The Coulomb Constant is #k=9*10^9Nm^2/C^2#

The charge #Q_1=6C# at #(-7,0)#

The charge #Q_2=-3C# at #(5,0)#

The charge #Q_3=-3C# at #(2,0)#

The overall force is

#F=910^9*(6*-3)/(9)^2+910^9(-3*-3)/(3)^2=9*10^9N#

The force is repulsive, as indicated by the positive sign.

Lily Adams · Answer

undefined Net force: 216 N towards -7.

Sebastian Acosta · Answer

undefined To find the net force on a charge of -3 C at a position of 2 units, we use Coulomb's Law, which states that the magnitude of the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The formula for Coulomb's Law is:

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

Where:
- $ F $ is the magnitude of the force between the charges.
- $ k $ is Coulomb's constant, approximately $ 8.9875 \times 10^9 \, N \cdot m^2/C^2 $.
- $ q_1 $ and $ q_2 $ are the charges.
- $ r $ is the distance between the charges.

Given that $ q_1 = 6 \, C $, $ q_2 = -3 \, C $, and $ r_1 = 2 \, m $ (distance from the charge of -3 C to the charge of 6 C), we can calculate the net force as follows:

$$ F_1 = k \cdot \frac{|6 \cdot (-3)|}{(5 - 2)^2} $$

$$ F_2 = k \cdot \frac{|(-3) \cdot (-3)|}{(2 + 7)^2} $$

The net force is the vector sum of $ F_1 $ and $ F_2 $. Since both forces act in opposite directions, the net force is the difference between their magnitudes.

$$ \text{Net force} = |F_1| - |F_2| $$

Finally, we need to determine the direction of the net force. Since $ F_1 $ is attractive (towards the positive charge) and $ F_2 $ is repulsive (away from the negative charge), the direction of the net force will be towards the positive charge.

Therefore, calculate $ F_1 $ and $ F_2 $, then find the net force as the difference between their magnitudes, and consider the direction towards the positive charge.