Question

The following problems consider the scalar form of Coulomb's law, which describes the electrostatic force between two point charges, such as electrons. It is given by the equation F(r)=ke|q1q2|r2,F(r)=ke|q1q2|r2, where keke is Coulomb's constant, qiqi are the magnitudes of the charges of the two particles, and rr is the distance between the two particles.

(a)

To simplify the calculation of a model with many interacting particles, after some threshold value r=R,r=R, we approximate ff as zero.

Explain the physical reasoning behind this assumption.

What is the force equation?

Evaluate the force FF using both Coulomb's law and our approximation, assuming two protons with a charge magnitude of 1.6022×10−19coulombs (C),1.6022×10−19coulombs (C), and the Coulomb constant ke=8.988×109Nm2/C2ke=8.988×109Nm2/C2 are 11 m apart. Also, assume R<1m.R<1m. How much inaccuracy does our approximation generate? Is our approximation reasonable?

Is there any finite value of RR for which this system remains continuous at RR?

Answer #1

According to the scalar form of Coulomb's law: the force acting between the 2 charged particles in inversely proportional to the square of the distance between them.So, as the distance increases the Electrostatic force decreases fast and at some Threshold value its magnitude is small enough that it can be neglected relative to the other forces acting on the charged particle due to interactions with other particles.

The Force equation is given by:

Force between 2 protons , 11 m apart given by Coulomb's law is:

As r=11m > R, using the approximation F(r)=0

**The inaccuracy generated by the approximation is of
which is very small in magnitude.**

**The approximation is thus
reasonable.**

To simplify the calculation of a model with many interacting
particles, after some threshold value ?=?,r=R, we approximate
F as zero.
Explain the physical reasoning behind this assumption.
What is the force equation?
Evaluate the force F using both Coulomb’s law and our
approximation, assuming two protons with a charge magnitude of
1.6022×10−19coulombs (C),1.6022×10−19coulombs (C), and the Coulomb
constant ??=8.988×10^9Nm2/C2 ke=8.988×10^9Nm2/C2 are 1 m apart.
Also, assume ?<1m. R<1m. How much inaccuracy does our
approximation generate? Is our approximation reasonable?...

Coulomb's law for the magnitude of the force FF between two
particles with charges QQ and Q′Q′ separated by a distance dd
is
|F|=K|QQ′|d2|F|=K|QQ′|d2,
where K=14πϵ0K=14πϵ0, and
ϵ0=8.854×10−12C2/(N⋅m2)ϵ0=8.854×10−12C2/(N⋅m2) is the permittivity
of free space.
Consider two point charges located on the x axis: one
charge, q1q1 = -13.0 nCnC , is located at x1x1 = -1.670 mm ; the
second charge, q2q2 = 39.0 nCnC , is at the origin (xx = 0).
What is (Fnet3)x(Fnet3)x, the x-component of the...

Coulomb's law for the magnitude of the force F between two
particles with charges Q and Q′ separated by a distance d is
|F|=K|QQ′|d2, where K=14πϵ0, and ϵ0=8.854×10−12C2/(N⋅m2) is the
permittivity of free space. Consider two point charges located on
the x axis: one charge, q1 = -10.0 nC , is located at x1 = -1.695 m
; the second charge, q2 = 31.0 nC , is at the origin
(x=0.0000).
What is the net force exerted by these two...

Coulomb's law for the magnitude of the force F between two
particles with charges Q and Q′ separated by a distance d is
|F|=K |QQ'|/d2
where K=1/4πϵ0 , and
ϵ0=8.854×10-12
C2/(N⋅m2) is the permittivity of free
space.
Consider two point charges located on the x axis: one
charge, q1 = -17.0 nCn, is located at X1 = -1.680 m ;
the second charge, q2 = 30.0 nC , is at the origin (x = 0).
What is (Fnet3)x, the x-component...

Coulomb's law for the magnitude of the force F between
two particles with charges Q and Q′separated by a
distance d is
|F|= (K) |QQ′| /
d2
where K=1 / 4πϵ0, and
ϵ0=8.854×10−12 C2 /
(N⋅m2) is the permittivity of free space.
Consider two point charges located on the x axis: one
charge, q1 = -13.5 nC , is located at
x1 = -1.745 m ; the second charge,
q2 = 31.5 nC ,is at the origin
(x=0.0000).
What is the...

Coulomb's law for the magnitude of the force F FF between two
particles with charges Q QQ and Q ′ Q′Q^\prime separated by a
distance d dd is |F|=K |Q Q ′ | d 2 |F|=K|QQ′|d2 , where K= 1 4π ϵ
0 K=14πϵ0 , and ϵ 0 =8.854× 10 −12 C 2 /(N⋅ m 2 )
ϵ0=8.854×10−12C2/(N⋅m2) is the permittivity of free space. Consider
two point charges located on the x axis: one charge, q 1 q1q_1 =
-20.0...

Coulomb's law for the magnitude of the force F between
two particles with charges Q
and Q′ separated by a distance d
is
|F|=K|QQ′|d2,
where K=14πϵ0, and
ϵ0=8.854×10−12C2/(N⋅m2) is the permittivity of free
space.
Consider two point charges located on the x axis: one
charge, q1 = -14.5 nC , is located at x1 = -1.655
m ; the second charge, q2 = 33.5 nC , is at the origin
(x=0.0000).
What is the net force exerted by these two charges on...

Coulomb's law for the magnitude of the force F between two
particles with charges Q and Q′ separated by a distance d is
|F|=K(|QQ′|/d^2)
where K=1/(4πϵ0), and ϵ0=8.854×10^−12 C^2/(N⋅m^2) is the
permittivity of free space.
Consider two point charges located on the x axis: one
charge, q1 = -17.5 nC , is located at x1= -1.735 mm ; the second
charge, q2 = 36.5 nC , is at the origin (x = 0).
What is (Fnet3)x, the x-component of the...

4. Electrostatics Coulomb’s law, or Coulomb’s inverse-square
law, is a law of physics that describes force interactions between
static electrically charged particles. The law is:
F=kq1q2r2whereq1andq2represent two charges separated by a distance
r and k is a constant approximately equal to 9×109Nm2C−2.
(a) Find the work required to bring together a 0.8nCnegative
charge and a 0.6nCnegative charge from a distance of 200 mm (0.2 m)
to a distance of 100 mm (0.1 m).Note:1nC= 10−9CwhereCstands for
coulombs and nC stands for...

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