The electric field strength 1.5 cm from an electric dipole, on the axis of the dipole, is 1.5×105 N/C. If the dipole is replaced by a single charge, what magnitude charge in nC will give the same field strength 1.5 cm away?

Ch 23: The Electric Field

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 23: The Electric Field

Problema 5c

Capitolo 23, Problema 5c

The electric field strength 1.5 cm from an electric dipole, on the axis of the dipole, is 1.5×10⁵ N/C. If the dipole is replaced by a single charge, what magnitude charge in nC will give the same field strength 1.5 cm away?

Guida verificata passo dopo passo

Step 1: Understand the problem. The electric field strength at a distance of 1.5 cm from a single charge is given as 1.5×10^5 N/C. We need to determine the magnitude of the charge (in nC) that produces this field strength.

Step 2: Recall the formula for the electric field due to a point charge:

E = \frac{k}{q} / r^{2}

, where

E

is the electric field strength,

k

is Coulomb's constant (

8.99 \times 10^9

N·m²/C²),

q

is the charge, and

r

is the distance from the charge.

Step 3: Rearrange the formula to solve for the charge

q

q = \frac{E}{\times} / k

. Substitute the given values:

E = 1.5 \times 10^{5}

N/C,

r = 0.015

m (converted from cm), and

k = 8.99 \times 10^{9}

N·m²/C².

Step 4: Perform the substitution into the formula:

q = \frac{1.5}{\times} / 8.99 \times 10^{9}

. Ensure all units are consistent (meters for distance, N/C for field strength).

Step 5: Convert the result for

q

into nanocoulombs (nC) by multiplying the value in coulombs by

10^9

. This will give the magnitude of the charge in nC that produces the same field strength.

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Electric Field

The electric field is a vector field that represents the force exerted by an electric charge on other charges in its vicinity. It is defined as the force per unit charge and is measured in newtons per coulomb (N/C). The strength of the electric field decreases with distance from the charge, following an inverse square law for point charges.

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03:16

Intro to Electric Fields

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance. The electric field produced by a dipole varies with distance and direction, and on the axis of the dipole, it can be calculated using specific formulas. Understanding dipoles is crucial for analyzing how they influence the electric field in their surroundings.

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03:08

Intro To Dipole Moment

Coulomb's Law

Coulomb's Law describes the force between two point charges and is fundamental in electrostatics. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is essential for calculating the electric field generated by a single charge at a given distance.

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Coulomb's Law

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