Three fixed charges are located along a line. The - 2 C charge is 10cm to the left of the +5 C charge and the -4 C charge at 4 cm to the right of the +5 C charge.
a.what is the force exerted on the -4 C by the +5C charge?
b.what is the force exerted on the -4 C by the -2 C charge?
c.what is the net force exerted on the -4 C charge?
let q1= -2C, q2= +5C, q3= -4C
also r13=10+4=14cm=0.14m
& r23= 4cm = 0.04m
a) Force on q3 due to q2:
F32= k*q3*q2/(r23)^2 towards left
b)Force on q3 due to q1:
F31= k*q3*q1/(r13)^2 towards right
c) Net force on q3 = F32-F31
To solve this problem, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Coulomb's Law is represented by the equation:
F = k * (|q1| * |q2|) / r^2
Where F is the force between the charges, k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
a. To find the force exerted on the -4 C charge by the +5 C charge, we can use the equation mentioned above. We know that the magnitude of the +5 C charge is 5 C and the distance between the charges is 4 cm (0.04 m) since they are located 4 cm apart. Plugging these values into the equation, we have:
F = (8.99 x 10^9 Nm^2/C^2) * (5 C * 4 C) / (0.04 m)^2
Calculating this, we find:
F = 449,500 N
Therefore, the force exerted on the -4 C charge by the +5 C charge is 449,500 N.
b. Similarly, to find the force exerted on the -4 C charge by the -2 C charge, we use the same equation. The magnitude of the -2 C charge is 2 C, and the distance between the charges is 4 cm (0.04 m) since they are located 4 cm apart. Plugging these values into the equation, we have:
F = (8.99 x 10^9 Nm^2/C^2) * (2 C * 4 C) / (0.04 m)^2
Calculating this, we find:
F = 449,500 N
Therefore, the force exerted on the -4 C charge by the -2 C charge is also 449,500 N.
c. The net force exerted on the -4 C charge is the vector sum of the forces exerted by the +5 C and -2 C charges. Since they are both acting in the same direction (both attracting the -4 C charge), we can simply add their magnitudes to find the net force. The net force is calculated by:
Net force = Force exerted by the +5 C charge + Force exerted by the -2 C charge
Net force = 449,500 N + 449,500 N
Calculating this, we find:
Net force = 899,000 N
Therefore, the net force exerted on the -4 C charge is 899,000 N.