A dipole consists of two opposite charges (q and -q) separated by a fixed distance d. The dipol

step 1 Net force as a vector equals fx x hat plus f y hat F x is Q e x minus q e x x x hat thus f y is

A dipole consists of two opposite charges (q and -q)...

A dipole consists of two opposite charges $(q \text { and }-q)$ separated by a fixed distance $d$. The dipole is placed in an electric field in the $+x$ -direction of magnitude $E .$ The dipole axis makes an angle $\theta$ with the electric field as shown in the diagram. (a) Calculate the net electric force acting on the dipole. (b) Calculate the net torque acting on the dipole due to the electric forces as a function of $\theta$. Let counterclockwise torque be positive. (c) Evaluate the net torque for $\theta=0^{\circ}$ $\theta=36.9^{\circ},$ and $\theta=90.0^{\circ} .$ Let $q=\pm 3.0 \mu \mathrm{C}, d=7.0 \mathrm{cm}$ and $E=2.0 \times 10^{4} \mathrm{N} / \mathrm{C}$ FIGURE CANT COPY

A dipole consists of two opposite charges $(q \text { and }-q)$ separated by a fixed distance $d$. The dipole is placed in an electric field in the $+x$ -direction of magnitude $E .$ The dipole axis makes an angle $\theta$ with the electric field as shown in the diagram. (a) Calculate the net electric force acting on the dipole. (b) Calculate the net torque acting on the dipole due to the electric forces as a function of $\theta$. Let counterclockwise torque be positive. (c) Evaluate the net torque for $\theta=0^{\circ}$ $\theta=36.9^{\circ},$ and $\theta=90.0^{\circ} .$ Let $q=\pm 3.0 \mu \mathrm{C}, d=7.0 \mathrm{cm}$
and $E=2.0 \times 10^{4} \mathrm{N} / \mathrm{C}$
FIGURE CANT COPY

Key Concepts

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a finite distance. This fundamental concept helps in understanding how these charges interact with external electric fields and with each other, leading to interesting phenomena such as torque and potential energy alignment in the field.

Dipole Moment

The dipole moment is a vector quantity defined as the product of the magnitude of one of the charges and the separation distance between them. It points from the negative charge to the positive charge and determines the dipole’s interaction strength with an electric field, particularly influencing the torque experienced by the dipole.

Uniform Electric Field

A uniform electric field is characterized by having the same magnitude and direction at every point in space. When a dipole is placed in such a field, the forces on the individual charges are equal in magnitude but opposite in direction, which results in a net force of zero while still possibly creating a net torque.

Torque on a Dipole

The torque on an electric dipole in an external electric field arises because the forces acting on the two charges produce a rotational effect about the dipole’s center. This torque tends to align the dipole moment with the field and is mathematically given by the cross-product of the dipole moment and the electric field, leading to a magnitude that is proportional to the sine of the angle between them.

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