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An electric dipole consists of two opposite charge

 

An electric dipole consists of two opposite charges +/- q separated by a small distance (s). The product p=qs is called the dipole moment. The following figure shows an electric dipole perpendicular to an electric field E.(Figure 1)

 

 

Find an expression in terms of p and E for the magnitude of the torque that the electric field exerts on the dipole.

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

find the magnitude of the electric force that the water molecule exerts on the chlorine ion.

The dipole moment of the water molecule (H2O) is 6.17x10^-30 C · m. Consider a water molecule located at the origin whose dipole moment vector p points in the +x-direction. A chlorine ion (Cl−), of charge −1.60 *10-19 C, is located at x = 1.34 *10-9 m.

Find the magnitude and direction of the electric force that the water molecule exerts on the chlorine ion.

Assume that x is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis E = p/2πε0y3 can be used, where p is the dipole moment, and y is the distance between ions.

A) What is magnitude______N

B) Direction? +x-direction or -x-direction

C) Is this force attractive or repulsive?

 

An electric dipole is located along the y axis as shown in figure P24.48. The magnitude of its electric dipole moment is defined as p = 2 aq.

(a) At a point P, which is far from the dipole (r » a), shown that the electric potential is

.

(b) Calculate the radial component Er and the perpendicular component Eθ of the associated electric field. Note that Eθ = -(1/r)(∂V/∂θ). Do these results seem reasonable for

(c) θ=90º and 0º?

(d) For r = 0?

(e) For the dipole arrangement shown in Figure P24.48 express V in termes of Cartesian coordinates using r = (x2+y2)1/2 and

.

(f) Using these results and again taking r » a, calculate the field of components Ex and Ey.

An electric dipole is located along the y axis as shown in Figure P24.48. The magnitude of its electric dipole moment is defined as p = 2aq.

(a) At a point P, which is far from the dipole (r >> a), show that the electric potential is 

V =Kp cos θ /r2

 

(b) Calculate the radial component Er and the perpendicular component Eθ of the associated electric field. Note that Eθ = —(1/r) (∂V/∂r). Do these results seem reasonable for

(c) θ = 90° and 0°?

(d) For r= 0?

(e) For the dipole arrangement shown in Figure P24.48, express V in terms of Cartesian coordinates using r= (x2 + y2)1/2  and cosθ =y /(x2 + y2)1/2

and

(f) Using these results and again taking r>> a, calculate the field components; Ex and Ey. 

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