Point charges q1 = -4.5 nC and q2 = +4.5 nC are separated by 3.1 mm, forming an electric dipole. (b) The charges are in a uniform electric field whose direction makes an angle of 36.9° with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude 7.2 * 10^-9 N•m?

Verified step by step guidance

1. Identify the given values: charge magnitudes q1 and q2, separation distance d, angle \( \theta \) between the electric field and the dipole, and the torque \( \tau \).
2. Understand that the torque \( \tau \) on a dipole in a uniform electric field is given by the formula \( \tau = pE \sin(\theta) \), where \( p \) is the dipole moment and \( E \) is the electric field magnitude.
3. Calculate the dipole moment \( p \) using the formula \( p = qd \), where \( q \) is the magnitude of one of the charges and \( d \) is the separation between the charges.
4. Rearrange the torque formula to solve for the electric field magnitude \( E \): \( E = \frac{\tau}{p \sin(\theta)} \).
5. Substitute the values for \( \tau \), \( p \), and \( \sin(\theta) \) into the rearranged formula to find the magnitude of the electric field.

Key Concepts

Electric Dipole

An electric dipole consists of two equal and opposite point charges separated by a distance. The dipole moment, a vector quantity, is defined as the product of the charge and the distance between the charges. It characterizes the strength and orientation of the dipole in an electric field, influencing how it interacts with external fields.

Torque on a Dipole

The torque ( au) experienced by an electric dipole in an electric field is given by the equation τ = pE sin(θ), where p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field. This torque tends to align the dipole with the field, and its magnitude depends on the orientation and strength of the field.

Uniform Electric Field

A uniform electric field is one in which the electric field strength (E) is constant in both magnitude and direction throughout a region. In such fields, the force on a charge is consistent, leading to predictable motion. The uniformity simplifies calculations involving forces and torques on dipoles, as the field does not vary with position.