Three charges are at the corners of an isosceles triangle as...

Three charges are at the corners of an isosceles triangle as shown in Fig. E21.55. The $\pm 5.00 \mu \mathrm{C}$ charges form a dipole. (a) Find the force (magnitude and direction) the $-10.00 \mu \mathrm{C}$ charge exerts on the dipole. (b) For an axis perpendicular to the line connecting the $\pm 5.00 \mu \mathrm{C}$ charges at the midpoint of this line, find the torque (magnitude and direction) exerted on the dipole by the $-10.00 \mu \mathrm{C}$ charge.

Three charges are at the corners of an isosceles triangle as shown in Fig. E21.55. The $\pm 5.00 \mu \mathrm{C}$ charges form a dipole.
(a) Find the force (magnitude and direction) the $-10.00 \mu \mathrm{C}$ charge exerts on the dipole. (b) For an axis perpendicular to the line connecting the $\pm 5.00 \mu \mathrm{C}$ charges at the midpoint of this line, find the torque (magnitude and direction) exerted on the dipole by the $-10.00 \mu \mathrm{C}$ charge.

Key Concepts

Superposition Principle

The superposition principle in electrostatics asserts that the net force on any charge due to a system of other charges is the vector sum of the individual forces exerted by each charge independently. This principle allows complex charge interactions to be broken down into simpler parts, making the computation of resultant forces and torques tractable.

Force on Charges

The concept of force on charges involves calculating the vector sum of the forces acting on a charge due to other charges, using principles such as Coulomb's Law. The net force takes into account both the magnitude and direction of each individual interaction, and vector addition is used to combine these effects.

Torque on an Electric Dipole

Torque on an electric dipole in an external electric field arises due to the tendency of the dipole to align with the field. This torque is given by the cross product of the dipole moment and the electric field. It is a measure of the rotational effect about a pivot point, which is important for understanding the stability and orientation of dipoles in electric fields.

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electric force between charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. This principle is critical for determining the interactions between charged particles and is the foundation for calculating forces in electrostatics.

Electric Dipole

An electric dipole consists of two equal but opposite charges separated by a small distance. The dipole moment, a vector quantity, characterizes its strength and orientation. Understanding dipoles is essential in the study of molecular interactions, polarization, and the behavior of materials in external electric fields.

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