CHEGG In the final stages of production, a pharmaceutical is sterilized by heating it from 25 to 75C as it moves at 0.2 m/s through a straight thin-walled stainless steel tube of 12.7-mm diameter. A uniform heat flux is maintained by an electric resistance heater wrapped around the outer surface of the tube. If the tube is 10 m long, what is the required heat flux
Answer:
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A. The star is approaching you with the speed of 3000 km/s.
B. The star is approaching you with the speed of 30300 km/s.
C. The star is receding from you with the speed of 3000 km/s.
D. The star is receding from you with the speed of 30300 km/s.
Answer:
C. The star is receding from you with the speed of 3000 km/s
Explanation:
To get this answer we use the doppler effect equation . The formula for a receding emissor is given in the attachment.
We solve for V
V = 3x10⁶m/s
V = 3000km/s
We have the wavelength to be shifting towards red. Therefore we conclude that it is receding. We say the star is receding with speed of 3000km/s towards you.
Thank you!
(a) What type of charge distribution is inside the surface? a positively charged plane parallel to the end faces of the cylinder a positive line charge situated on and parallel to the axis of the cylinder a collection of positive point charges arranged in a line at the center of the cylinder and perpendicular to the axis of the cylinder a collection of negative point charges arranged in a line at the center of the cylinder and perpendicular to the axis of the cylinder a negatively charged plane parallel to the end faces of the cylinder (b) If the radius of the cylinder is 0.66 m and the magnitude of the electric field is 300 N/C, what is the net electric flux through the closed surface? N · m2/C (c) What is the net charge inside the cylinder? nC
Answer:
a) The type of charge distribution inside the surface is a negatively charged plane parallel to the end faces of the cylinder.
b) the net electric flux is -821.09 N.m²/c
c) the net charge inside the cylinder is -7.2666 nC
Explanation:
Given the data in the question;
a) (a) What type of charge distribution is inside the surface?
Based on the Image of the question below;
The type of charge distribution inside the surface is a negatively charged plane parallel to the end faces of the cylinder.
b) If the radius of the cylinder is 0.66 m and the magnitude of the electric field is 300 N/C, what is the net electric flux through the closed surface?
we know that; Electric flux is;
∅ = -2 × E × Area
we substitute
∅ = -2 × 300 × π ( 0.66 m )²
= -821.09 N.m²/c
Therefore; the net electric flux is -821.09 N.m²/c
c) What is the net charge inside the cylinder? nC
from Gause's law;
∅ = q/∈₀
q = ∅ ∈₀
we know permittivity ∈₀ = 8.85 × 10⁻¹²)
we substitute
q = -821.09 N.m²/c × (8.85 × 10⁻¹²)
q = -7.2666 × 10⁻⁹ C
q = -7.2666 nC
Therefore, the net charge inside the cylinder is -7.2666 nC
How much power does it take to lift 30.0 kg 100 m high in 5.00 s?
._.Answer:.
ijji._. ji
Explanation:.
In a particular metal, the mobility of the mobile electrons is 0.0033 (m/s)/(N/C). At a particular moment, the electric field everywhere inside a cube of this metal is 0.033 N/C in the x direction. What is the average drift speed of the mobile electrons in the metal at this moment
Answer:
the average drift speed of the mobile electrons in the metal is 1.089 x 10⁻⁴ m/s.
Explanation:
Given;
mobility of the mobile electrons in the metal, μ = 0.0033 (m/s)/(N/C)
the electric field strength inside the cube of the metal, E = 0.033 N/C
The average drift speed of the mobile electrons in the metal is calculated as;
v = μE
v = 0.0033 (m/s)/(N/C) x 0.033 N/C
v = 1.089 x 10⁻⁴ m/s.
Therefore, the average drift speed of the mobile electrons in the metal is 1.089 x 10⁻⁴ m/s.
In a series circuit of two resistors, the resistors have the same __________; in a parallel circuit of two resistors, the resistors have the same __________. In a series circuit of two resistors, the resistors have the same __________; in a parallel circuit of two resistors, the resistors have the same __________. Voltage across them, current through them Current through them, voltage across them Current through them, current through them Voltage across them, voltage across them
Answer:
Current through them, voltage across them.
Explanation:
Ohm's law states that at constant temperature, the current flowing in an electrical circuit is directly proportional to the voltage applied across the two points and inversely proportional to the resistance in the electrical circuit.
Mathematically, Ohm's law is given by the formula;
[tex] V = IR[/tex]
Where;
V represents voltage measured in voltage.
I represents current measured in amperes.
R represents resistance measured in ohms.
A resistor can be defined as an electronic component that opposes the free flow of current from one point to another in an electrical circuit.
In a series circuit of two resistors, the resistors have the same current through them; in a parallel circuit of two resistors, the resistors have the same voltage across them.
A baseball is hit when it is 2.5 ft above the ground. It leaves the bat with an initial velocity of 145 ft/sec at a launch angle of 23°. At the instant the ball is hit, an instantaneous gust of wind blows against the ball, adding a component of -14i (ft/sec) to the ball’s initial velocity. A 15-ft-high fence lies 300 ft from home plate in the direction of the flight.
a. Find a vector equation for the path of the baseball.
b. How high does the baseball go, and when does it reach maxi-mum height?
c. Find the range and flight time of the baseball, assuming that the ball is not caught.
d. When is the baseball 20 ft high? How far (ground distance) is the baseball from home plate at that height?
e. Has the batter hit a home run? Explain.
Answer:
Explanation:
Take base of the ground as origin .
component of initial velocity along i and j direction is 145 con23 and 145 sin23 . Along j , gravity acts but along i , no force acts .
The path of ball in vector form
s = (145 cos23- 14 )t i + ( 2.5 + 145sin23 t - 1/2 g t² ) j
t is time period .
b )
vertical component of initial velocity = 145 sin 23 =
for vertical displacement
v² = u² - 2gH
For maximum height , v = 0
0 = (145 sin 23 )² - 2 g H , H is maximum height attained .
H = 3209.56 / 2 x 9.8
= 163.75 m
Total height attained = 163.75 + 2.5 = 166.25 m
if time be t for reaching maximum height
v = u -gt
0 = 145 sin 23 - gt
t = 145 sin23 / g
= 5.78 s
c )
For time of flight , vertical displacement = 2.5 m
2.5 = - 145 sin 23 t + 1/2 g t²
2.5 = -56.65 t + 4.9 t²
4.9 t² - 56.65 t - 2.5 = 0
t = 11.60s
horizontal displacement during this period = 145 cos23 x 11.60 = 1548.28 m
Range = 1548.28 m.
In January 2017, when Clemson won the football championship, Coach Dabo Swinney decided to buy pizza for all students at Clemson to celebrate. So, From his office(Death Valley), he drove 100 m North to reach HWY 93, 200 m East to reach the 133 Junction(Downtown) and 500 m North to reach Papa John's to place his order. What was the total displacement of Coach Swinney
Answer:
Explanation:
We shall represent each move of coach in vector form , considering unit vector i towards east and unit vector j towards north .
he drove 100 m North
First displacement D₁ = 100 j
200 m East to reach the 133
second displacement D₂ = 200 i
500 m North to reach Papa John's
third displacement
D₃ = 500 j
Total displacement ( resultant displacement )
= D₁ + D₂ + D₃
= 100 j + 200 i + 500 j
= 200 i + 600 j
magnitude of resultant displacement
= √ ( 200² + 600² )
= √ 40000 + 360000
= 632.45 m
What is one example of an individual in an ecosystem?
Answer:
a
Explanation:
AAAA
What is the efficiency of a machine that has an output work of 1675 J and an input work
of 1895 J?
Answer:
1.13%
explanation:
work output/work input =100%
In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at 73.5 m/s. The driver of the Thunderbird realizes that she must make a pit stop, and she smoothly slows to a stop over a distance of 250 m. She spends 5.00 s in the pit and then accelerates out, reaching her previous speed of 73.5 m/s after a distance of 400 m. At this point how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed
Answer:
Thunderbird has fallen behind the Mercedes Benz by 1017.49 m
Explanation:
Given the data in question;
initial speed of the ford u1 = 73.5 m/s
distance d1 = 250 m
t1 = 5.00 s
d2 = 400 m
Now, let the time taken to stop be t2 and deceleration is a1
so,
a1 = u1² / (2 × d1)
a1 = (73.5)² / (2 × 250)
a1 = 10.8045 m/s²
Now , for acceleration is a2
a2 = v² / (2 × d2)
a2 = (73.5)² / (2 × 400)
a2 = 6.7528 m/s²
total time spend = 5 + u/a1 + u/a2
total time spend = 5 + (73.5/10.8045) + (73.5/6.7528)
total time spend = 22.687 sec
Now, distance Mercedes is ahead = 22.687 × 73.5 - 400 - 250
= 1667.4945 - 400 - 250
= 1017.49 m
Therefore, Thunderbird has fallen behind the Mercedes Benz by 1017.49 m
Explain what is happening in this picture
Answer:
in this video waves are coming up for the BOTTOM to the top of the sandbar
Which sequence correctly shows an increase in potential energy
Answer:
The heavier the object and the higher it is above the ground, the more gravitational potential energy it holds. Gravitational potential energy increases as weight and height increases. Potential energy is energy that is stored in an object or substance.
A 0.14 kg baseball moving at 23.00 m s is slowed to a stop by a catcher who exerts a constant force of 370 N How long does it take this force to stop the ball Incorrect Your answer is incorrect s How far does the ball travel before stopping
Answer:
(A) The time taken for the ball to stop is 8.7 x 10⁻³ s
(B) The distance traveled by the baseball before stopping is 0.3 m
Explanation:
Given;
mass of the baseball, m = 0.14 kg
velocity of the baseball, v = 23 m/s
force exerted on the baseball by the catcher, F = 370 N
(A) The time taken for the ball to stop;
[tex]F = ma = \frac{mv}{t} \\\\t = \frac{mv}{F} \\\\t = \frac{0.14 \times 23}{370} \\\\t = 8.7\times 10^{-3} \ s\\\\t = 8.7 \ ms[/tex]
(B) The distance traveled by the baseball before stopping is calculated as;
acceleration of the ball, [tex]a = \frac{v}{t} = \frac{23}{8.7\times 10^{-3}} = 2643.678 \ m/s^2[/tex]
Distance traveled, s;
s = ut + ¹/₂at²
s = (23)(8.7 x 10⁻³) + ¹/₂(2643.678)(8.7 x 10⁻³)²
s = 0.2001 + 0.1001
s = 0.3 m
A 28.8 kg child sits on a 6.0 m long teeter-totter at a point 1.5 m from the pivot point (at the center of the teeter-totter). On the other side of the pivot point, an adult pushes straight down on the teeter-totter with a force of 180 N. Determine the direction the teeter-totter will rotate if the adult applies the force at a distance of each of the following from the pivot. (Assume the teeter-totter is horizontal when the adult applies the force and that the child's weight applies a clockwise torque.)
a.
1. 1.0 m
2. counterclockwise
b.
1. 2.0 m
2. clockwise
3. counterclockwise
c.
1. 3.0m
2. clockwise
3. counterclockwise
Answer:
case A) tau_net = -243.36 N m, case B) tau_net = 783.36 N / m, tau_net = -63.36 N m, case C) tau _net = - 963.36 N m,
Explanation:
For this exercise we use Newton's relation for rotation
Σ τ = I α
In this exercise the mass of the child is m = 28.8, assuming x = 1.5 m, the force applied by the man is F = 180N
we will assume that the counterclockwise turns are positive.
case a
tau_net = m g x - F x2
tau_nett = -28.8 9.8 1.5 + 180 1
tau_net = -243.36 N m
in this case the man's force is downward and the system rotates clockwise
case b
2 force clockwise, the direction of
the force is up
tau_nett = -28.8 9.8 1.5 - 180 2
tau_net = 783.36 N / m
in case the force is applied upwards
3) counterclockwise
tau_nett = -28.8 9.8 1.5 + 180 2
tau_net = -63.36 N m
system rotates clockwise
case c
2 schedule
tau_nett = -28.8 9.8 1.5 - 180 3
tau _net = - 963.36 N m
3 counterclockwise
tau_nett = -28.8 9.8 1.5 + 180 3
tau_net = 116.64 Nm
the sitam rotated counterclockwise
What are the two rules that light follows.
ok so i dont know srry5
How many boron atoms are there in 5 molecules of BF3? Hint: The symbol for boron is B. Submit
Answer:
5 atoms of Boron
Explanation:
Boron makes up approximately 15.944% of the mass and the rest of the 84.056% is Fluorine. There is 5 Atoms because Boron atomic mass is 10.811 in 1 molecule of BF3 and you wanted 5 Molecules.
To see the number of atoms of an element in a given molecule we need to multiply stoichiometry to the number that is written on the foot of the element that is stoichiometry. Therefore, in 5 molecules of BF[tex]_3[/tex], the number of boron atoms is 5.
What is atom?Atom is the smallest particle of any element, molecule or compound. Atom can not be further divided. Atoms contains nucleus in its center and electron that revolve around the atom in fixed orbit.
In the nucleus, proton and neutron are present. Electron has -1 charge while proton has +1 charge. Neutron is neutral that is it has no charge. So overall the charge of nucleus is due to only proton, not by neutron.
In one molecule of BF[tex]_3[/tex], the number of boron atoms is 1. So, in 5 molecules of BF[tex]_3[/tex], the number of boron atoms is 5.
Therefore, in 5 molecules of BF[tex]_3[/tex], the number of boron atoms is 5.
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Anyone know this question?
A flashlight beam makes an angle of 60 degrees with the surface of the water before it enters the water. In the water what angle does the beam make with the surface
Answer:
θ₂ = 40.5º
Explanation:
For this exercise we must use the law of refraction
n₁ sin θ₁ = n₂ sin θ₂
where index 1 is for the incident ray and index 2 is for the refracted ray
in this case the incident ray has an angle of θ₁ = 60º and the refractive index of the water is
n₂ = 1,333
sin θ₂ = [tex]\frac{n_1}{n_2} \ sin \theta_1[/tex]
let's calculate
sin θ₂ = 1 / 1.3333 sin 60
sin θ₂ = 0.64968
θ₂ = sin⁻¹ (0.64968)
θ₂ = 40.5º
In an early attempt to understand atomic structure, Niels Bohr modeled the hydrogen atom as an electron in uniform circular motion about a proton with the centripetal force caused by Coulomb attraction. He predicted the radius of the electron's orbit to be 5.29 ✕ 10−11 m. Calculate the speed of the electron and the frequency of its circular motion.
Answer:
The answer is below
Explanation:
Using Coulomb's law of electric field which is:
[tex]F=k\frac{q_1q_1}{r^2}\\\\ k =constant=9*10^9\ Nm^2/C^2,q_1=q_2=1.6*10^{-19}C,r=5.29*10^{-11}m\\\\Substituting\ gives:\\\\F=9*10^9*\frac{(1.6*10^{-19})*(1.6*10^{-19})}{(5.29*10^{-11})^2} =8.22*10^{-8}N\\\\Both\ centripetal\ force\ is\ given\ by:\\\\F=m\frac{v^2}{r} \\\\m = mass\ of \ electron=9.11*10^{-31}g,v=speed\ of\ electron\\\\F=m\frac{v^2}{r} \\\\v=\sqrt{\frac{F*r}{m} } \\\\subsituting:\\\\v=\sqrt{\frac{8.22*10^{-8}*5.29*10^{-11}}{9.11*10^{-31}} } \\\\v=2.18*10^6\ m/s\\\\[/tex]
[tex]But\ \omega=\frac{v}{r}=\frac{2.18*10^6}{5.29*10^{-11}} =4.13*10^{17}\\\\\omega=2\pi f; f=frequency\\\\f=\frac{\omega}{2\pi} =\frac{4.13*10^{17}}{2\pi} \\\\f=6.57*10^{15}\ Hz[/tex]
What is the main cause of ocean currents? Question 2 options:
The prevailing winds
The Coriolis effect
Waves
The sun and the moon
A fairgrounds ride spins its occupants inside a flying saucer-shaped container. If the horizontal circular path the riders follow has a 9.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration whose magnitude is 1.80 times that due to gravity
Answer:
13.37 rev/min
Explanation:
acceleration due to gravity (g) = 9.8 m/s², centripetal acceleration ([tex]a_c[/tex]) = 1.8 * g = 1.8 * 9.8 m/s² = 17.64 m/s².
r = 9 m
Centripetal acceleration ([tex]a_c[/tex]) is given by:
[tex]a_c=\frac{v^2}{r} \\\\v=\sqrt{a_c*r} \\\\v=\sqrt{17.64\ m/s^2*9\ m}\\\\v=12.6\ m/s[/tex]
The velocity (v) is given by:
v = ωr; where ω is the angular velocity
Hence:
ω = v/r = 12.6 / 9
ω = 1.4 rad/s
ω = 2πN
N = ω/2π = 1.4 / 2π
N = 0.2228 rev/s
N = 13.37 rev/min
What is the speed of a sailboat traveling 100m in 140s?
Answer:
Explanation:
d = rt only works for calculating average speeds.
100 = r(140)
r = 0.714 m/s
Answer: 0.71m/s
Explanation:
Formula: Speed = Distance/time
Speed = 100m/140s
Speed = 100/140 / 20/20
Speed = 5/7 or 0.71m/s
When external forces acting on an object are balanced, what will happen to the object's
motion?
(7 Points)
The object will speed up.
The object will slow down.
The object will change direction.
The object's motion will remain the same
The object will stop
Answer:
The objects morion will remain the same
Explanation:
g In an historical movie, two knights on horseback start from rest 84.1 m apart and ride directly toward each other to do battle. Sir George's acceleration has a magnitude of 0.316 m/s2, while Sir Alfred's has a magnitude of 0.289 m/s2. Relative to Sir George's starting point, where do the knights collide?
Answer:
The knights will collide at 43.854 meters relative to Sir George's starting point.
Explanation:
Let suppose that initial positions of Sir George and Sir Alfred are 0 and 84.1 meters, respectively. If both knights accelerate uniformly, then we have the following kinematic formulas:
Sir George
[tex]x_{G} = x_{G,o}+v_{o,G}\cdot t + \frac{1}{2}\cdot a_{G}\cdot t^{2}[/tex] (1)
Sir Alfred
[tex]x_{A} = x_{A,o}+v_{o,A}\cdot t + \frac{1}{2}\cdot a_{A}\cdot t^{2}[/tex] (2)
Where:
[tex]x_{G,o}[/tex], [tex]x_{A,o }[/tex] - Initial position of Sir George and Sir Alfred, measured in meters.
[tex]x_{G}[/tex], [tex]x_{A}[/tex] - Final position of Sir George and Sir Alfred, measured in meters.
[tex]v_{o,G}[/tex], [tex]v_{o,A}[/tex] - Initial velocity of Sir George and Sir Alfred, measured in meters per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]a_{G}[/tex], [tex]a_{A}[/tex] - Acceleration of Sir George and Sir Alfred, measured in meters per square second.
Both knights collide when [tex]x_{G} = x_{A}[/tex], then we simplify this system of equations below:
[tex]x_{G,o} + v_{o,G}\cdot t + \frac{1}{2}\cdot a_{G}\cdot t^{2} = x_{A,o}+v_{o,A}\cdot t + \frac{1}{2}\cdot a_{A}\cdot t^{2}[/tex]
[tex](x_{A,o}-x_{G,o}) +(v_{o,A}-v_{o,G})\cdot t +\frac{1}{2}\cdot (a_{A}-a_{G})\cdot t^{2} = 0[/tex] (3)
If we know that [tex]x_{A,o} = 84.1\,m[/tex], [tex]x_{G,o} = 0\,m[/tex], [tex]v_{o,A} = 0\,\frac{m}{s}[/tex], [tex]v_{o,G} = 0\,\frac{m}{s}[/tex], [tex]a_{A} = -0.289\,\frac{m}{s^{2}}[/tex] and [tex]a_{G} = 0.316\,\frac{m}{s^{2}}[/tex], then we have the following formula:
[tex]84.1 -0.303\cdot t^{2} = 0[/tex] (4)
The time associated with collision is:
[tex]t \approx 16.660\,s[/tex]
And the point of collision is:
[tex]x_{G} = 0\,m + \left(0\,\frac{m}{s} \right)\cdot (16.660\,s)+ \frac{1}{2}\cdot \left(0.316\,\frac{m}{s^{2}} \right) \cdot (16.660\,s)^{2}[/tex]
[tex]x_{G} = 43.854\,m[/tex]
The knights will collide at 43.854 meters relative to Sir George's starting point.
A scalar is a mathematical term for:
a. measurement
b. Magnitude and Direction
c. A number and a unit
d. A Scale
Answer:
c. A number and a unit
Explanation:
A scalar is a real number. We often use the term scalar in the context of vectors or matrices, to stress that a variable such as a is just a real number and not a vector or matrix.
Explain the physics of carnival rides in terms of motion, forces, energy, and momentum
Answer:
it spins
Explanation:
like a lot, bro i was on one before and it was pretty nice :)
What are the units of the slope of a velocity-time graph?
Answer: m/s
Explanation:
The slope is the change in y over the change in x. If the graph is velocity over time, then the units will be meters per second
If two people, mass of 70 kg and 85 kg respectively, approach each other with speeds of 4 m/s and 7 m/s, what is the total momentum of the two person system? Give the momentum of each and then the total momentum.
Answer:
a. Momentum A = 280 Kgm/s.
b. Momentum B = 595 Kgm/s.
c. Total momentum = 875 Kgm/s.
Explanation:
Let the two people be A and B respectively.
Given the following data;
Mass A = 70kg
Mass B = 85kg
Velocity A = 4m/s
Velocity B = 7m/s
Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.
Mathematically, momentum is given by the formula;
[tex] Momentum = mass * velocity [/tex]
a. To find the momentum of A;
[tex] Momentum \; A = 70 * 4 [/tex]
Momentum A = 280 Kgm/s.
b. To find the momentum of B;
[tex] Momentum \; B = 85 * 7 [/tex]
Momentum B = 595 Kgm/s.
c. To find the total momentum of the two persons;
[tex] Total \; momentum = Momentum \; A + Momentum \; B [/tex]
Substituting into the equation, we have;
[tex] Total momentum = 280 + 595 [/tex]
Total momentum = 875 Kgm/s.
An electron is accelerated through 2400 V from rest and then enters a region in which there is a uniform 1.70 T magnetic field. What are (a) the maximum and (b) the minimum magnitudes for the magnetic force this charge can experience
Answer:
Explanation:
Let v be the velocity acquired by electron in electric field
V q = 1/2 m v²
V is potential difference applied on charge q , m is mass of charge , v is velocity acquired
2400 x 1.6 x 10⁻¹⁹ = .5 x 9.1 x 10⁻³¹ x v²
v² = 844 x 10¹²
v = 29.05 x 10⁶ m /s
Maximum force will be exerted on moving electron when it moves perpendicular to magnetic field .
Maximum force = Bqv , where B is magnetic field , q is charge on electron and v is velocity of electron
= 1.7 x 1.6 x 10⁻¹⁹ x 29.05 x 10⁶
= 79.02 x 10⁻¹³ N .
Minimum force will be zero when electron moves along the direction of magnetic field .
(a) The maximum force on the electron due to the magnetic field will be F= 79.02 x 10⁻¹³ N .
(b) Minimum force will be zero when electron moves along the direction of magnetic field .
What is magnetic force?Whenever a current is passes through a wire then the magnetic fields are generated around the wire and if any other charged particle comes under the influence of this magnetic field then the magnetic force is applied in the charge.
Let v be the velocity acquired by an electron in electric field
[tex]Vq=\dfrac{1}{2}mv^2[/tex]
V is potential difference applied on charge q ,
m is mass of charge ,
v is velocity acquired
2400 x 1.6 x 10⁻¹⁹ = .5 x 9.1 x 10⁻³¹ x v²
v² = 844 x 10¹²
v = 29.05 x 10⁶ m /s
Maximum force will be exerted on the moving electron when it moves perpendicular to the magnetic field .
Maximum force = Bqv , where B is magnetic field , q is charge on an electron and v is velocity of electron
F=Bqv
F= 1.7 x 1.6 x 10⁻¹⁹ x 29.05 x 10⁶
F= 79.02 x 10⁻¹³ N .
Minimum force will be zero when electron moves along the direction of magnetic field .
Hence the maximum force on the electron due to the magnetic field will be F= 79.02 x 10⁻¹³ N and the Minimum force will be zero when electron moves along the direction of magnetic field .
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