Fig. 3 shows an electric dipole in a uniform electric field with magnitude 10 × 105

N/C directed parallel to the plane of the figure. The electric dipole consists of two
charges 𝑞1 = +2𝑒 and 𝑞2 = −2𝑒 ( 𝑒 = 1.6 × 10−19), which both lie in the plane and
separated by a distance 0.13𝑛𝑚.
3.1 Find
3.1.1 the net force exerted by the field on the dipole
3.1.2 the magnitude and direction of the electric dipole moment
3.1.3 the magnitude and direction of the Torque
3.1.4 the potential energy of the system in position shown in Fig. 3.

1 answer

To find the net force exerted by the field on the dipole, we need to consider the electric field experienced by each charge in the dipole.

The electric field experienced by charge q1 is given by:
E1 = k * (q1 / r1^2)
where k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 is the charge of q1 (+2e = 2 * 1.6 x 10^-19 C), and r1 is the distance from q1 to the center of the dipole.

The electric field experienced by charge q2 is given by:
E2 = k * (q2 / r2^2)
where q2 is the charge of q2 (-2e = -2 * 1.6 x 10^-19 C) and r2 is the distance from q2 to the center of the dipole.

Since the electric field is uniform, the magnitudes of E1 and E2 are equal.

Using the formula for the net force on a dipole in an electric field, we have:
F = Δp * E
where Δp is the electric dipole moment and E is the electric field.

The electric dipole moment (p) is given by:
p = q * d
where q is the magnitude of either charge (2e = 2 * 1.6 x 10^-19 C) and d is the separation between the charges (0.13 nm = 0.13 x 10^-9 m).

To find the magnitude and direction of the torque, we use the formula:
τ = p * E * sin(θ)
where θ is the angle between the dipole moment and the electric field.

Finally, the potential energy of the system is given by:
U = -p * E * cos(θ)

Now let's calculate these values:

3.1.1 The net force exerted by the field on the dipole:
First, we need to calculate the magnitudes of E1 and E2:

E1 = k * (q1 / r1^2) = (9 x 10^9 Nm^2/C^2) * (2e / (0.13 x 10^-9 m)^2)
E1 = 9 x 10^9 Nm^2/C^2 * (2 * 1.6 x 10^-19 C) / (0.13 x 10^-9 m)^2

Similarly,
E2 = k * (q2 / r2^2) = (9 x 10^9 Nm^2/C^2) * (-2e / (0.13 x 10^-9 m)^2)
E2 = 9 x 10^9 Nm^2/C^2 * (-2 * 1.6 x 10^-19 C) / (0.13 x 10^-9 m)^2

Since the electric field is uniform, the net force is the product of Δp and E:

F = Δp * E
F = (q * d) * (E1 - E2)

3.1.2 The magnitude and direction of the electric dipole moment:
p = q * d

3.1.3 The magnitude and direction of the torque:
τ = p * E * sin(θ)

3.1.4 The potential energy of the system:
U = -p * E * cos(θ)

Note: In order to fully solve the problem and provide specific numerical calculations, the values of q, d, r1, and r2 are needed.