In an hyperbola, the fixed points that have a constant difference in distance from the center are called _ A. Asymptotes
B. Centers
C. Foci
D. Vertices

Please select the best answer from the choices provided

OA
OB
OC
OD

The correct answer is C. Foci.

A hyperbola is defined as the flat open curve resulting from the intersection of a right circular cone from a plane not parallel to any of its origins. The line joining the foci of the hyperbola is called the base line.

The perpendicular to the middle of the baseline is called the center line. It becomes apparent that all points of the center line are equidistant from the foci.

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The magnitude of the force on the dipole due to the charge Q =

The magnitude of the torque on the dipole =

Explanation:

Given that a point charge Q is held at a distance r from the center of a dipole that consists of two charges ±q, separated by a distance s and the charge Q is located in the plane that bisects the dipole.

The magnitude of the electric field that the dipole exerts at the position where the charge Q is held is given by

where,

k is the Coulomb's constant, having value =

is the electrical permittivity of free space.

Also, r>>s, therefore,

The magnitude of the electric force F on a charge q placed at a point and the magnitude of the electric field E at that point are related as

Therefore, the electric force on the charge Q due to the dipole is given by

According to Newton's third law of motion, the magnitude of the force exerted by the dipole on the charge Q is same as the magnitude of the force exerted by the charge on the dipole.

Thus, the magnitude of the force on the dipole due to the charge Q =

The magnitude of the torque on the dipole is given by

Since the charge Q is placed in the plane that bisects the dipole, therefore, .