To understand the origin of the torque on a current loop due to the magnetic forces on the current-carrying wires.

This problem will show you how to calculate the torque on a magnetic dipole in a uniform magnetic field. We start with a rectangular current loop, the shape of which allows us to calculate the Lorentz forces explicitly. Then we generalize our result. Even if you already know the general formula to solve this problem, you might find it instructive to discover where it comes from.

a) Give a more general expression for the magnitude of the torque τ. Rewrite the answer found in Part A in terms of the magnitude of the magnetic dipole moment of the current loop m. Define the angle between the vector perpendicular to the plane of the coil and the magnetic field to be ϕ, noting that this angle is the complement of angle θ in Part A.

Give your answer in terms of the magnetic moment m, magnetic field B, and ϕ.

Answers

Answer 1

Answer:

The torque is  [tex]\tau = B * m sin(\phi )[/tex]

Explanation:

Generally when current flow through a rectangular loop the magnetic dipole generated we can denote this as  [tex]\vec m[/tex]

Here k is the length of the side of one side of the rectangular loop

Now when this loop is place in a magnetic field, the torque it experience is mathematically represented as

      [tex]\vec \tau = \vec B \ X \ \vec m[/tex]

Here  X stands for cross - product

From the question we are told that the angle between the vector ( [tex]\vec m[/tex])perpendicular to the plane of the coil and magnetic field(B) as [tex]\phi[/tex]

So

=>     [tex]\tau = B * m sin(\phi )[/tex]


Related Questions

Please help A.S.A.P
What would you expect to see on intrusive igneous rocks compared to extrusive igneous rocks?

Answers

Answer:

Intrusive igneous rocks cool from magma slowly because they are buried beneath the surface, so they have large crystals. Extrusive igneous rocks cool from lava rapidly because they form at the surface, so they have small crystals. Texture reflects how an igneous rock formed

Explanation:

how do you find circular motion?​

Answers

Answer:

Explanation:

By multiplying the rotational frequency with the circumference we can determine the average speed of the object. The circular velocity formula is expressed as, vc = 2 πr / T. Where in, r denotes the radius of the circular orbit. T is time period.

Answer:

2πr

as we know that the circumference of a circle is 2 * π * r, the arc length of the whole circle is 2πr units. Then using the formula s = r * theta, the angle theta equals the arc length divided by the radius. Therefore theta = 2πr/r = 2π radians.

I hope it will helpful for you

mark as brainest answer

thank you

What happens to the sound an object makes when the speed of vibrtions decreases (slowdown?)

Answers

Answer:

the volume increase

Explanation:

because because when the speed of the vibrations decrease the speech of the sounds become loud

One particle has a charge of 4.2 x 10-9 C, while another particle has a charge
of 1.10 x 10-9 C. If the two particles are separated by 0.005 m, what is the
electromagnetic force between them? The equation for Coulomb's law is
Fe = k992, and the constant, k, equals 9.00 x 109 Nm2/C2.
A. 8.31 x 10-6N
B. 1.66 x 10-5 N
C. 1.85 10-13 N
D. 1.66 10-3 N

Answers

Answer:

D

Explanation:

Answer:

The forces between the charges is [tex]1.66*10^{-3} N[/tex]

Explanation:

Data given:

First charge [tex]q_{1} =4.2*10^{-9} C[/tex]

Another charge [tex]q_{2} =1.1*10^{-9} C[/tex]

Distance (r)= (0.005)m

Force(F)=?

It is based on Electrostatic force between two charges i.e. defined by Coulomb's law.

What is electrostatic force?

The force acting between two static charges, is called electrostatic force.

What is Coulomb's law?

The force acting between two charges is

(a) directly proportional to the product of charges F ∝ [tex]q_{1} q_{2}[/tex]

(b) inversely proportional to the square of the separation. F ∝ [tex]\frac{1}{r^{2} }[/tex]

From above;

[tex]F=k.\frac{q_{1} q_{2} }{r^{2} }[/tex]

On putting values: -

[tex]F=1.66*10^{-3} N[/tex]

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what are some solutions to global temperature changes?
help asap​

Answers

Answer:

Power your home with renewable energy.

Weatherize, weatherize, weatherize.

Invest in energy-efficient appliances.

Reduce water waste.

Actually eat the food you buy—and make less of it meat.

Explanation:

what do you notice from the picture?​

Answers

What I notice in the picture is some type of scientists examining a animal and making guesses on what it could be

What one would notice from the picture depend on the view point and the perspective of the person because different people looking at this elephant would notice a different thing according to their perception.

What is perspective?

Perspective refers to how one views things. It is a method of art that modifies the size or depth of an item on paper. Farm owners' perspectives on a shortage of rain are an illustration of perception. In a picture, the train tracks appear to curve into the horizon as an illustration of perspectives.

For the person looking from the front elephant's teeth would appear like a spear, for the person looking at its leg would imagine a tree , for the person on the ladder the big structure of the elephant would appear like a wall,the person looking from the back on its tail would imagine it as a rope.

Thus, perspective is very crucial when we are looking at different things from different angles.

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an automobile was moving at 15m/s and accelerated at 2m/s^2 for 10s. what is the final speed

Answers

Answer:

35 m/s

Explanation:

Given that an automobile was moving at 15m/s and accelerated at 2m/s^2 for 10s. what is the final speed ?

The parameters given are :

initial velocity U = 15 m/s

Acceleration a = 2 m/s^2

Time taken = 10s

Using first equation of motion;

V = U + at

V = 15 + 2 * 10

V = 15 + 20

V = 35 m/s

Therefore, The final speed is 35 m/s

The final speed of automobile moving at the given initial speed and acceleration is 35m/s.

Given the data in the question;

Initial velocity of the automobile; [tex]u = 15m/s[/tex]Acceleration of the automobile; [tex]a = 2m/s^2[/tex]Time taken; [tex]t = 10s[/tex]

Final velocity of the automobile; [tex]v = ?[/tex]

To determine the final velocity of the automobile, we use the First Equation of Motion:

[tex]v = u + at[/tex]

Where v is final velocity, u is initial velocity, a is acceleration and t is time taken.

We substitute our given values into the equation

[tex]v = 15m/s + [ 2m/s^2 * 10s ]\\\\v = 15m/s + 20m/s\\\\v = 35m/s[/tex]

Therefore, the final speed of automobile moving at the given initial speed and acceleration is 35m/s.

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How long would it take to swim across a lake that is 350 meters, if you swam at 9 m/sec

Answers

Answer:

[tex]\boxed {\tt t\approx 38.89 \ s}[/tex]

Explanation:

Time can be found by dividing the distance by the speed.

[tex]t=\frac{d}{s}[/tex]

The distance is 350 meters.

The speed is 9 meters per second.

[tex]d= 350 \ m \\s= 9 \ m/s[/tex]

Substitute the values into the formula.

[tex]t=\frac{350 \ m}{9 \ m/s}[/tex]

Divide. Note that the meters or "m" will cancel each other out and the seconds or "s" will move to the numerator.

[tex]t=\frac{350 }{9 \ s}[/tex]

[tex]t=\frac{350 \ s}{9}[/tex]

[tex]t=38.8888889 \ s[/tex]

Round to the nearest hundredth. The 8 in the thousandth place tells us to round the 8 to a 9.

[tex]t \approx38.89 \ s[/tex]

It will take about 38.89 seconds to swim 350 meters at 9 meters per second.

An elephant of mass 100kg stands with all four foots on the ground.Each foot covers an area of 0.04m2.calculate the pressure exerted on the ground.​

Answers

Answer:

140KG

Explanation:

To decorate for a party, Simon needs 1,850 centimeters of colorful streamers. If the ratio of meters to centimeters is 1 : 100, how many meters of streamers does he require?

A.
18,500 meters
B.
185 meters
C.
18.5 meters
D.
1.85 meters

Answers

C because 1,850 divided by 100 is 18.50 but since zeros do not matter in decimals ( unless it is money ) we can removes the zero making it 18.5 meters

A lever has a total length of 12 meters with a fulcrum at the exact center of the lever. Which best describes how to

double the mechanical

advantage of the lever?

O Move the fulcrum 2 meters away from the side on which the force is applied.

Move the fulcrum 2 meters toward the side on which the force is applied.

O Move the fulcrum 4 meters away from the side on which the force is applied.

O Move the fulcrum 4 meters toward the side on which the force is applied.

Answers

Answer:

The correct option is the last option.

Explanation:

Generally, when trying to create a mechanical advantage of a lever for an apparatus or a machine, the load is usually moved closer to the fulcrum. Hence, if a lever has a total length of 12 meters and the fulcrum is placed at 6 meters (the center), the best way (based on the previous statement) to double the mechanical advantage of the lever is to move the fulcrum 4 meters toward the side on which the force is applied. The correct option is the last option.

Answer: the answer  is  not  d  idk wat it is sorry but its not d

how many apples are in 29 trees if each tree has 45 apples?

Answers

Answer:

1305 I think but not sure

Its 1305 because 29 x 45 = 1305

12. A screwdriver is which type of a simple machine?
O wedge
O screw
O wheel and axle
O lever

Answers

Answer:

wheel and axle

Explanation:

hope this helps

If the Mass Number is the sum of the protons and neutrons in an atom, what is
the mass number of

Answers

Answer:

It's 31

Explanation:

add 15 and 16

A cheetah can run at a maximum speed 103 km/h and a gazelle can run at a maximum speed of 76.5 km/h. If both animals are running at full speed, with the gazelle 99.3 m ahead, how long before the cheetah catches its prey?

Answer in units of s.


Part 2: The cheetah can maintain its maximum speed for only 7.5 s. What is the minimum distance the gazelle must be ahead of the cheetah to have a chance of escape? (After 7.5 s the speed of cheetah is less than that of the gazelle.)

Answer in units of m.

Answers

Answer:

1

 [tex] t_a  =  13.49 \  s   [/tex]

2

 The distance is   [tex] D = 55.2 \  m  [/tex]    

Explanation:

From the question we are told that

   The maximum speed of the cheetah is  [tex]v =  103 \  km/h =  28.61 \  m/s[/tex]

    The maximum of  gazelle is  [tex]u =  76.5 \  km/h =  21.25 \  m/s[/tex]

     The distance ahead is [tex]d =  99.3 \  m[/tex]

Let  [tex]t_a[/tex] denote the time which the cheetah catches the gazelle

Gnerally the equation representing the distance the cheetah needs to move in order to catch the gazelle is

           [tex] v* t_a = d +  u* t_a [/tex]

=>          [tex] 28.61 t_a = 99.3 +  21.25t_a [/tex]

=>          [tex] 7.36 t_a = 99.3  [/tex]

=>         [tex] t_a  =  13.49 \  s   [/tex]

Now at t =  7.5 s  

             [tex]7.5 v = D+  7.5u [/tex]

=>          [tex] 28.61 * 7.5  = D +  21.25* 7.5  [/tex]

=>          [tex] 7.36 *  7.5 =D  [/tex]

=>         [tex] D = 55.2 \  m  [/tex]        

Hence the for the gazelle to escape the cheetah it must be 55.2 m

how permeable and porous would an aquifer be?

Answers

Answer: An aquifer is a body of saturated rock through which water can easily move. Aquifers must be both permeable and porous and include such rock types as a sandstone.

Explanation: However, if these rocks are highly fractured, they make good aquifers.

What special name is given to group II elements in the periodic table?

Answers

Answer:

Alkaline earth metals.

Explanation:

For e.g The metals of group ll are: Be, Mg, Ca, etc

Alkaline earth metals

Acceleration is the rate of change in the speed of an object. To determine the rate of acceleration, you use the formula below. The units for acceleration are meters per second per second or m/s2.

Answers

Explanation:

Acceleration is the rate of change in the speed of an object. If initial and final speed are v₁ and v₂. It changes speed in time t. Its formula is given by :

[tex]a=\dfrac{v_2-v_1}{t}[/tex]

The problem is "A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s acceleration? "

In this problem,

v₁ = 2 , v₂ = 10 m/s and t = 3 s

Acceleration of the object,

[tex]a=\dfrac{10-2}{3}\\\\a=2.67\ m/s^2[/tex]

So, the acceleration of the skater is [tex]2.67\ m/s^2[/tex].

How can you explain why there are so many hours of darkness on December 21? How can you explain why there are so many hours of daylight on June 21?

Answers

Answer:

At the december solstice,the northern hemisphere is leaning most away from the sun for the year.At the december solatric,earth is positioned in its orbit so that the sun below the north pole horizon. After the winter solstice,the days get longer,and the night shorter.

What is his average acceleration from 10 to 20 seconds

Answers

Answer:-2.0

Explanation:khan academy

The picture is my question

Answers

c                                                                                                                                                  cccccccccccccccccccccccccccccccccccccccccccccccccccccc

1 point
An Arizona solar power plant is able to produce 24 megawatts, which
serves 6,000 homes. How many watts per home?
40 W
О
400 W
4,000 W
40,000 W

Answers

the answer is 4,000 because there are 1 million watts per mega wat so 24x1,000,000 = 24,000,000 / 6,000= 4,000

Define measurement.​

Answers

Answer:

The process of comparison of unknown quantity with the help of known standard quantity is known as measurement...Hope this helps:)

Answer:

the comparison of an unknown quantity with the known quantity.

Explanation:

...........................................................................................................................

If a ball has a mass of 224 grams and a volume of 53ml, what is the density of the ball? Please round your answer to the nearest tenth.​

Answers

Answer:

The answer is 4.2 g/mL

Explanation:

The density of a substance can be found by using the formula

[tex]density = \frac{mass}{volume} \\ [/tex]

We have

[tex]density = \frac{224}{53} \\ = 4.2264150943396...[/tex]

We have the final answer as

4.2 g/mL to the nearest tenth

Hope this helps you

Answer:

The density is 4.2

Explanation:

D=M/V

Density is equal to mass/Volume thus D=M/V


A branch swept into a Category 3 hurricane has a centripetal acceleration of 0.028 m/s2. Estimate the radius of the storm is wind speeds are
53 m/s

Answers

Answer:

Radius, r = 100321.43m or 10.03 * 10^4m

Explanation:

Given the following data;

Acceleration, a = 0.028m/s²

Speed = 53m/s

Centripetal acceleration is given by the formula;

[tex] Acceleration, a = \frac {v^{2}}{r}[/tex]

Substituting into the equation, we have;

[tex] Acceleration, a = \frac {53^{2}}{0.028}[/tex]

[tex] Acceleration, a = \frac {2809}{0.028}[/tex]

Radius, r = 100321.43m or 10.03 * 10^4m

Forces may cause an object to change ____ if it is unable to move

Answers

Answer:

Motion

Acceleration is the change of velocity per unit time, so if there is no force, all we know is that the acceleration is zero. Therefore, the velocity is not changing. If the object was already moving, then it will just keep moving. So, the object can be moving even when there is no force applied to it.

Forces may cause an object to change its state if it is unable to move. The force make the object to move from its state of rest.

What is force?

Force is an external agent acting on an object to deform it or to change it state of rest or motion. There are various kinds of forces such as gravitational force, nuclear force, magnetic force, frictional force etc.

Force is a vector quantity thus, it is characterised by its magnitude and direction. According to Newton's first law of motion, an object will continue in its state or motion or rest until an external force acts on it.

Therefore, force changes the state of an object. Force is dependant on the mass of the object. Greater the mass, greater will be the force required to move the object from stationary to stop it from motion.

According to second law of motion, force is the product of mass and acceleration of the object. Hence, force accelerates the body and a change in force changes the acceleration of the object.

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The electron affinity of thulium has been measured by a technique known as laser photodetachment electron spectroscopy. In this technique, a gaseous beam of the anions of an element is bombarded with photons from a laser. Electrons from the anion are then ejected and their energies are detected. The incident radiation had a wavelength of 1064 nm, and the ejected electrons were found to have an energy of 0.137 eV. The electron affinity is the difference in energy between the incident photons and the energy of the ejected electrons. Determine the electron affinity of thulium in units of electron volts per atom.

Answers

Answer:

ΔE = 1.031 eV

Explanation:

For this exercise let's calculate the energy of the photons using Planck's equation

          E = h f

wavelength and frequency are related

         c = λ f

         f = c /λ

let's substitute

         E = h c /λ

let's calculate

         E = 6.63 10⁻³⁴ 3 10⁸/1064 10⁻⁹

         E = 1.869 10⁻¹⁹ J

let's reduce to eV

         E = 1.869 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)

        E = 1.168 eV

therefore the electron affinity is

         ΔE = E - 0.137

         ΔE = 1.168 - 0.137

         ΔE = 1.031 eV

The electron affinity of thulium in units of electron volts per atom is; ΔE ≈ 1.031 eV

From Planck's equation, we can find the energy of the photons when given wavelength as;

E = hc/λ

Where;

h is Planck's constant = 6.626 × 10⁻³⁴ J.s

c is speed of light = 3 × 10⁸ m/s

λ is wavelength

We are given;

wavelength; λ = 1064 nm = 1064 × 10⁻⁹ m

Thus;

E = (6.626 × 10⁻³⁴ × 3 × 10⁸)/(1064 × 10⁻⁹)

E2 = 1.868 × 10⁻¹⁹ J

Converting to eV gives;

E2 = (1.868 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹)

E2 = 1.1675 eV

We are given E1 = 0.137 eV.

Now, electron affinity is simply change in energy. Thus;

ΔE = 1.1675 - 0.137

ΔE ≈ 1.031 eV

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Which quantities define momentum?
A. How much matter an object has, plus the magnitude and direction
of its motion
B. How much weight an object has, plus the magnitude of its
acceleration
C. How much force is pushing an object, plus its speed
D. How fast an object is traveling, plus its weight

Answers

Answer:

A. How much matter an object has, plus the magnitude and direction  of its motion

Explanation:

Momentum is defined as the product of mass by velocity, in the international system of measurements (SI) momentum has the following Units [kg*m/s].

P = m*v

where:

P = momentum Lineal [kg*m/s]

m = mass [kg]

v = velocity [m/s]

Therefore the answer is A) How much matter an object has, plus the magnitude and direction  of its motion

Answer:

A is correct

Explanation:

A P E X

I don’t know why I am feeling worse day by day!

Answers

Answer:

Why ?? What happened ??

How much force is required to accelerate a 0.145 kg baseball to 150 m/s2?

Answers

Force = 0.145 x 150 = .... N
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