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Viktor [21]
3 years ago
5

If the total charge on a rod of length 0.4 m is 2.6 nc, what is the magnitude of the electric field at a location 3 cm from the

midpoint of the rod?
Physics
1 answer:
Nana76 [90]3 years ago
3 0
Let the rod be on the x-axes with endpoints -L/2 and L/2 and uniform charge density lambda (2.6nC/0.4m = 7.25 nC/m). 

The point then lies on the y-axes at d = 0.03 m. 

from symmetry, the field at that point will be ascending along the y-axes. 


A charge element at position x on the rod has distance sqrt(x^2 + d^2) to the point. 

Also, from the geometry, the component in the y-direction is d/sqrt(x^2+d^2) times the field strength. 


All in all, the infinitesimal field strength from the charge between x and x+dx is: 


dE = k lambda dx * 1/(x^2+d^2) * d/sqrt(x^2+d^2) 


Therefore, upon integration, 


E = k lambda d INTEGRAL{dx / (x^2 + d^2)^(3/2) } where x goes from -L/2 to L/2. 


This gives:


E = k lambda L / (d sqrt((L/2)^2 + d^2) ) 


But lambda L = Q, the total charge on the rod, so 


E = k Q / ( d * sqrt((L/2)^2 + d^2) )
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As a laudably skeptical physics student, you want to test Coulomb's law. For this purpose, you set up a measurement in which a p
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distance, r = 911 nm = 911 x 10^-9 m

The Coulomb's force is given by

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F=\frac{9\times 10^{9}\times 1.6\times 10^{-19}\times 1.6\times 10^{-19}}{\left (911\times 10^{-9}  \right )^2}

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A 0.325 g wire is stretched between two points 57.7 cm apart. The tension in the wire is 650 N. Find the frequency of first harm
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Answer:

f = 931.1 Hz

Explanation:

Given,

Mass of the wire, m = 0.325 g

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Tension in the wire, T = 650 N

Frequency for the first harmonic = ?

we know,

v =\sqrt{\dfrac{T}{\mu}}

μ is the mass per unit length

μ = 0.325 x 10⁻³/ 0.577

μ = 0.563 x 10⁻³ Kg/m

now,

v =\sqrt{\dfrac{650}{0.563\times 10^{-3}}}

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The wire is fixed at both ends. Nodes occur at fixed ends.

For First harmonic when there is a node at each end and the longest possible wavelength will have condition

          λ=2 L

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we now,

       v = f λ

      f = \dfrac{v}{\lambda}

      f = \dfrac{1074.49}{1.154}

             f = 931.1 Hz

The frequency for first harmonic is equal to f = 931.1 Hz

7 0
3 years ago
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