Question

The figure below shows an electric dipole in a uniform electric field with magnitude 5.0 × 105 N/C directed parallel to the plane of the paper. The molecular electric dipole p placed in this field has charges ±1.6 × 10−19 C, and they are separated by a distance of 0.125 nm. (a) Find the net force exerted by the field on the dipole. 2 (b) Find the magnitude and direction of the electric dipole moment. 2 (c) Find the magnitude and direction of the torque. 3 (d) Find the potential energy of the system in the position shown.

Answer 1

(a) The net force exerted by the electric field on the dipole is
`\(8.0 * 10^(-12)\)` N, directed from the positive to the negative charge.

(b) The electric dipole moment has a magnitude of
`\(2.0 * 10^(-29)\)`C·m, directed from the negative to the positive charge.

(c) The torque exerted on the dipole is
`\(1.0 * 10^(-20)\)` N·m, directed perpendicular to both the electric field and the dipole moment.

Explaination:

In the given scenario, an electric dipole is placed in a uniform electric field with a magnitude of
`\(5.0 * 10^5 \, \text{N/C}\) directed parallel to the plane of the paper. The dipole consists of charges \(+1.6 * 10^(-19) \, \text{C}\) and \(-1.6 * 10^(-19) \, \text{C}\), separated by a distance of \(0.125 \, \text{nm}\).`

(a) The net force exerted on the dipole is determined by the electric field strength and the separation of charges. The formula
`\(F = qE\) gives \(8.0 * 10^(-12) \, \text{N}\)`, with the direction from the positive to the negative charge.

(b) The electric dipole moment
`(\(p\))`is calculated using the formula \
`(p = q \cdot d\),`resulting in
`\(2.0 * 10^(-29) \, \text{C}\cdot\text{m}\),`directed from the negative to the positive charge.

(c)
`The torque (\(\tau\)) acting on the dipole in a uniform electric field is given by \(\tau = p \cdot E \cdot \sin\theta\), where \(\theta\) is the angle between \(p\) and \(E\). In this case, the torque is \(1.0 * 10^(-20) \, \text{N}\cdot\text{m}\), directed perpendicular to both \(E\) and \(p\).`

(d) The potential energy
`(\(U\))` of the system is given by
`\(U = -p \cdot E \cdot \cos\theta\),`where
`\(\theta\)`is the angle between
`\(p\) and \(E\).`In the given position, the potential energy is not provided, so it cannot be determined without additional information.