Chapter 23: Q. 6 (page 653)

An electric dipole is formed from $\pm 1.0 nC$ charges spaced apart. The dipole is at the $2.0 mm$ origin, oriented along the $x$ -axis. What is the electric field strength at the points (a) $(x, y) = (10 cm, 0 cm)$ and $(b) (x, y) = (0 cm, 10 cm)$ $?$

Short Answer

Expert verified

a.Electric field strength at point $(x, y) = (10 cm, 0 cm)$ is ${\vec{E}}_{x} = 36 N / C (i)$ .

b.Electric field strength at point role="math" localid="1649114602807" $(x, y) = (0 cm, 10 cm)$ is $18 N / C (- j)$ .

Step by step solution

Formula for electric field with dipole

Moment of dipole

$\vec{p} = q \vec{d}$

The dipole's electric field on its axis is:

$E_{dipole} \approx \frac{1}{4 {πϵ}_{o}} \frac{2 \vec{p}}{r^{3}}$

The dipole's electric field on its bisector is:

$E_{dipole} \approx - \frac{1}{4 {πϵ}_{o}} \frac{\vec{p}}{r^{3}}$

q is charge.

$\vec{d}$ is displacement vector.

$\vec{p}$ is dipole moment vector.

localid="1649113793496" $r$ is distance between the point and the dipole's centre.

Calculation of electric field (part a)

(a).

Dipole moment is,

$\vec{p} = (1.0 \times 10^{- 9} C) (2.0 \times 10^{- 3} m)$

$\vec{p} = 2.0 \times 10^{- 12} C \cdot m i$

At point $(x, y) = (10 cm, 0 cm)$

Because the point is on the dipole's axis, it is on the $x$ -axis.

${\vec{E}}_{x} = \frac{1}{4 {πϵ}_{0}} \frac{2 \times (2.0 \times 10^{- 12} C \cdot m)}{(0.1 m)^{3}}$

${\vec{E}}_{x} = 36 N / C (i)$

Calculation of electric field strength (part b)

(b).

At point $(x, y) = (0 cm, 10 cm)$

Because the point is on the dipole's bisector, it is on the $y$ -axis.

${\vec{E}}_{y} = - \frac{1}{4 {πϵ}_{o}} \frac{(2.0 \times 10^{- 12} C \cdot m)}{(0.1 m)^{3}}$

${\vec{E}}_{y} = 18 N / C (- j)$

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An electric dipole is formed from $\pm 1.0 nC$ charges spaced apart. The dipole is at the $2.0 mm$ origin, oriented along the $x$ -axis. What is the electric field strength at the points (a) $(x, y) = (10 cm, 0 cm)$ and $(b) (x, y) = (0 cm, 10 cm)$ $?$

Short Answer

Step by step solution

Formula for electric field with dipole

Calculation of electric field (part a)

Calculation of electric field strength (part b)

One App. One Place for Learning.

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An electric dipole is formed from ±1.0nCcharges spaced apart. The dipole is at the 2.0mmorigin, oriented along the x-axis. What is the electric field strength at the points (a) (x,y)=(10cm,0cm)and(b)(x,y)=(0cm,10cm)?

Short Answer

Step by step solution

Formula for electric field with dipole

Calculation of electric field (part a)

Calculation of electric field strength (part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Measurements

Conservation of Energy and Momentum

Kinematics Physics

Waves Physics

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.

An electric dipole is formed from $\pm 1.0 nC$ charges spaced apart. The dipole is at the $2.0 mm$ origin, oriented along the $x$ -axis. What is the electric field strength at the points (a) $(x, y) = (10 cm, 0 cm)$ and $(b) (x, y) = (0 cm, 10 cm)$ $?$