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FinnZ [79.3K]
3 years ago
8

A positive point charge (q 7.2 108 C) is surrounded by an equipotential surface A, which has a radius of rA 1.8 m. A positive te

st charge (q0 4.5 1011 C) moves from surface A to another equipotential surface B, which has a radius rB. The work done as the test charge moves from surface A to surface B is WAB8.1 109 J. Find rB.
Physics
1 answer:
Minchanka [31]3 years ago
4 0
<h2>Thus the radius r_{B} is 1.2 m</h2>

Explanation:

The potential at point A due to point charge at center .

V₁ = \frac{q}{4\pi\epsilon_0r_A } =  7.2 x 10⁻⁸ x 9 x 10⁹ [\frac{1}{r_A}]

Similarly

The potential at B

V₂ = \frac{q}{4\pi\epsilon_0r_B } = 7.2 x 10⁻⁸ x 9 x 10⁹ [ \frac{1}{r_B} ]

The potential difference

V = V₂ - V₁ = 648  [ \frac{1}{r_B} - \frac{1}{r_A} ]

The work done

W = q₀ V = 4.5 x 10⁻¹¹ x 648 [\frac{1}{r_B} - \frac{1}{r_A} ]

But W = 8.1 x 10⁻⁹ J

Thus equation is

8.1 x 10⁻⁹ = 4.5 x 10⁻¹¹ x 648 [\frac{1}{r_B} - \frac{1}{r_A} ]

0.28 = [ \frac{1}{r_B} - \frac{1}{1.8} ]  or  \frac{1}{r_B} = 0.28 + 0.55 = 0.83

or r_{B} =  1.2 m

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8 0
4 years ago
Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.8×106N , one an angle 11degrees west of north an
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Answer: 2,9 ×10¹⁰J.

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1. The <em><u>work </u></em>is a measure of energy and is calculated as the product of the displacement times the parallel force to such displacement.

That means that the only components of the force that contribute to work are those that result parallel to the displacement.

2. Since it is given that the <em>two tugboats "pull the tanker a distance 0.83km toward the north"</em>, that is the displacement, and you have to calculate the net force toward the north.

3. <u>Tugboat #1</u>.

a) Force magnitude: F₁ = 1.8×10⁶N

b) Angle: α = 11° West of North

c) North component of the force F₁: Fy₁ = F₁cos(α) =  1.8×10⁶N  × cos(11°) = 1.77×10⁶N

4. <u>Tugboat #2</u>:

a) Force magnitude: F₂ = 1.8×10⁶N

b) Angle:  = 11° East of North

c) North component of the force F₂: Fy₂ = F₂cos(β) =  1.8×10⁶N  × cos(11°) = 1.77×10⁶N =

5. <u>Total net force, Fn</u>:

Fn = Fy₁ + Fy₂ = 1.77×10⁶N + 1.77×10⁶N = 3.54×10⁶N

6. <u>Work, W</u>:

Displacement, d = 0.83 km = 8,300 m

W = Fn×d = 3.54×10⁶N×8,300m = 29,000 ×10⁶J = 2,9 ×10¹⁰J

The answer is rounded to two significant figures because both data, Force and displacement, have two significant figures.

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