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Lena
2 months ago
9

Three equal negative point charges are placed at three of the corners of a square of side d. What is the magnitude of the net el

ectric field at the center of the square? (k=1/4πϵ0=8.99×109N⋅m2/C2 )
Express your answer in terms of the variables d, q, and appropriate constants.
Physics
2 answers:
Ostrovityanka [3.2K]2 months ago
8 0
<span>this might be useful
Regarding the field, the two charges placed opposite cancel each other out!
Therefore, E = kQ / d² = k * Q / (d/√2)² = 2*k*Q / d² ◄
given k = 8.99×10^9 N·m²/C²,
E = 1.789×10¹⁰ N·m²/C² * Q / d² </span>
Ostrovityanka [3.2K]2 months ago
7 0

Answer:

E = 2kq / d²

Explanation:

Let the side length of the square be d.

The distance from the center to a corner, a, is calculated as:

a = √(d² + d²) / 2

a = √(2d²) / 2

a = (√2 * d) / 2

a = d / √2

Electric field magnitude is:

E = kq / a²

Substituting a = d / √2, yields:

E = kq / (d / √2)²

E = kq / (d² / 2)

E = 2kq / d²

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In circuit analysis, various essential physical quantities must be accurately measured to define circuit characteristics. These include current, denoted as I, representing the flow of electrons, and voltage, which indicates potential difference within the circuit. Most crucially, the resistance, R, outlines the circuit parameters. All these measurements can be determined using a digital multimeter or DMM.
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19 days ago
When the displacement of a mass on a spring is 1/2a the half of the amplitude, what fraction of the mechanical energy is kinetic
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Total energy associated with a spring:
E = \frac{1}{2} kx^2 + \frac{1}{2} mv^2 = \frac{1}{2} ka^2

When x = 0.5a:
\frac{1}{2} k \frac{a}{2} ^2 + \frac{1}{2} mv^2 = \frac{1}{2} ka^2 \\ \frac{1}{2} mv^2 = \frac{1}{2} ka^2 - \frac{1}{8} ka^2 = \frac{3}{8} ka^2

The ratio:
\frac{ \frac{3}{8}ka^2 }{ \frac{1}{2} ka^2} = \frac{3}{4}
5 0
21 day ago
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A 54 kg man holding a 0.65 kg ball stands on a frozen pond next to a wall. He throws the ball at the wall with a speed of 12.1 m
serg [3582]

Response:

The man's speed is 0.144 m/s

Explanation:

This exemplifies conservation of momentum.

The momentum of the ball prior to being caught must equal the momentum of the man-ball system after catching the ball.

Mass of the ball = 0.65 kg

Mass of the man = 54 kg

Speed of the ball = 12.1 m/s

The momentum of the ball before impact can be calculated as mass multiplied by velocity

= 0.65 x 12.1 = 7.865 kg-m/s

After catching the ball, the momentum of the combined system is

(0.65 + 54)Vf = 54.65Vf

Where Vf denotes their final shared velocity.

Setting the initial momentum equal to the final momentum,

7.865 = 54.65Vf

Vf = 7.865/54.65 = 0.144 m/s

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A 250 GeV beam of protons is fired over a distance of 1 km. If the initial size of the wave packet is 1 mm, find its final size
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Answer:

The final size is nearly the same as the initial size because the increase in size1.055\times 10^{- 7} is remarkably small

Solution:

According to the problem:

The proton beam energy is E = 250 GeV =250\times 10^{9}\times 1.6\times 10^{- 19} = 4\times 10^{- 8} J

Distance traveled by the photon, d = 1 km = 1000 m

Proton mass, m_{p} = 1.67\times 10^{- 27} kg

Initial size of the wave packet, \Delta t_{o} = 1 mm = 1\times 10^{- 3} m

Now,

This operates under relativistic principles

The rest mass energy for the proton is expressed as:

E = m_{p}c^{2}

E = 1.67\times 10^{- 27}\times (3\times 10^{8})^{2} = 1.503\times 10^{- 10} J

This proton energy is \simeq 250 GeV

Thus, the speed of the proton, v\simeq c

The time to cover 1 km = 1000 m of distance is calculated as:

T = \frac{1000}{v}

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\Delta t_{o} = \Delta t

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Response:

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Details:

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