Charge A has a charge of +2C. Charge B has a charge of -3C and is located 1 meter to the right of A. Charge C is located 1 meter to the right of Charge B and has a charge of -1C. If a fourth charge (Charge D) is placed 4 meters to the right of Charge B, how much charge must it have for the Net Force on Charge B to be zero?

If the net force on Charge B is zero, => the electric field strength is zero at the point B (charge B location).

vector E(A) +vector E(C) +vector E(D) = 0 =>
At the point B:
Vectors E(A) and E(C) are direcred to the right =>
vector E(D) has to be directed to the left => charge D is positive.

kq(A)/r(AB)²+ kq(C)/r(BC)²= kq(D)/r(BD)²
2/1²+ 1/1² =q(D)/4²
q(D) = + 48 C

To determine the charge required for Charge D to make the net force on Charge B zero, we can use Coulomb's Law and the principle of superposition.

Coulomb's Law 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.

Let's first calculate the individual forces exerted on Charge B by Charges A and C.

Force between A and B (F₁):
Using Coulomb's Law,
F₁ = k * (|charge A| * |charge B|) / (distance AB)²
where k is the Coulomb's constant (k = 9 × 10^9 N m²/C²).

Plugging in the values:
F₁ = (9 × 10^9 N m²/C²) * (2C * 3C) / (1m)²
F₁ = 54N

Note that the direction of force F₁ is attractive, since Charge A is positive and Charge B is negative.

Force between B and C (F₂):
Similarly,
F₂ = k * (|charge B| * |charge C|) / (distance BC)²
F₂ = (9 × 10^9 N m²/C²) * (3C * 1C) / (1m)²
F₂ = 27N

Note that the direction of force F₂ is repulsive, since both Charge B and Charge C are negative.

Now, to find the net force on Charge B, we consider the forces F₁ and F₂. Since F₁ is directed to the left and F₂ is directed to the right, the net force will be the difference between them:

Net Force on B (F_net) = F₁ - F₂
F_net = 54N - 27N
F_net = 27N to the left

To make the net force on Charge B zero, we need Charge D to exert a force of 27N to the right on B.

Using Coulomb's Law, we can calculate the required charge of Charge D:

F₃ = k * (|charge B| * |charge D|) / (distance BD)²

Plugging in the values:
27N = (9 × 10^9 N m²/C²) * (3C * |charge D|) / (4m)²

Simplifying the equation and solving for |charge D|:
|charge D| = (27N * (4m)²) / ((9 × 10^9 N m²/C²) * (3C))
|charge D| ≈ 3.2 × 10^-9 C

To make the net force on Charge B zero, Charge D should have a charge of approximately 3.2 × 10^-9 C.