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Write an equation for the magnetic field vector b generated by the current at an arbitrary point in terms of i, the length eleme

Lubov Fominskaja [6]

The magnetic field vector B generated by the current at an arbitrary point in terms of i, the length element dl, and the vector for the distance r from dl to the point is given by the equation dB = μ0/4 π ∫ (dl x r)/r $r^{3}$

<h3>Biot – Savart Law and its Applications:</h3>

The Biot – Savart Law gets its name from Jean-Baptiste Biot and Felix Savart. This is a formula that describes the relationship between force, displacement, and velocity. It plays a huge role in the branch of electromagnetism. This law is used to derive the equation between the magnetic field which is produced due to the flow of a constant electric current.

The equation of Biot – Savart law is

dB = μ0/4 π ∫ {(idl sinΦ)/r2}

Here,

I is the current,

dl is the small length of the wire. As the direction of this length is along the current hence it forms the vector idl.

r is the position vector of the point in question which is drawn from the current element and

Φ is the angle between the two.

<h3>Applications of Biot – Savart Law </h3>

• It helps in the calculation of magnetic field in an infinitely long straight wire with constant current,

• Calculation of magnetic field in the center of current carrying arc can be done by this,

• To calculate the magnetic field along the axis of a circular current carrying coil, this law can be used.

To know more about Biot - Savart Law visit:

brainly.com/question/14950341

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3 0

1 year ago

For a proton in the ground state of a 1-dimensional infinite square well, what is the probability of finding the proton in the c

Butoxors [25]

Answer:

The probability of finding the proton at the central 2% of the well is almost exactly 4%

Explanation:

If we solve Schrödinger's equation for the infinite square well, we find that its eigenfunctions are sinusoidal functions, in particular, the ground state is a sinusoidal function for which only half a cycle fits inside the well.

let $L$ be the well's length, the boundary conditions for the wavefunction are:

$\psi(0) = \psi(L) =0$

And Schrödinger's equation is:

$- \frac{\hbar^2}{2m} \frac{d^2\psi}{dx^2} = E\psi$

The solution to this equation are sines and cosines, but the boundary conditions only allow for sine waves. As we pointed out, the ground state is the sine wave with the largest wavelength possible (that is, with the smallest energy).

$\psi_0(x)=\sqrt[]{\frac{2}{L} }\, \sin(\frac{\pi x}{L} )\\$

here the leading constant is just there to normalise the wavefunction.

Now, if we know the wavefunction, we can know what the probability density function is, it is:

$f_X(x) = |\psi|^2$

So in our case:

$f_X(x) = \frac{2}{L} \sin^2(\frac{\pi x}{L})$

And to find the probability of finding the particle in a strip at the centre of the well of width 2% of L we only have to integrate:

$P(X \in [0.49 L, 0.51L ])= \int\limits^{0.49L}_{0.51L } {\frac{2}{L} \sin^2(\frac{\pi x}{L})} \, dx$

If we do a substitution:

$x = u \, L$

We get the integral:

$\int\limits^{0.49}_{0.51 } 2\, \sin^2(\pi u)} \, du$

This integral can be computed analytically, and it's numerical value is .0399868, that is, almost a 4% probability.

5 0

3 years ago

Select the correct statement about osmolarity. a) Osmolarity measures the moles of solute per liter of solution. b) The contents

8090 [49]

Answer:

a) Osmolarity measures the moles of solute per liter of solution.

Explanation:

Osmolarity is defined as the number of moles of solute that contribute to the osmotic pressure, per liter of solution, of solution. That is, the measurement of the solute concentration. The prefix "osmo-" indicates the possible variation of the osmotic pressure in the cells, which will occur when the solution is introduced into the body.

7 0

4 years ago

What is the weigh in newtons of an automobile with a mass of 1800 kg?

Allushta [10]

Answer:

The weight of an automobile, W = 17640 N

Explanation:

Given that,

The mass of an automobile, m = 1800 Kg

The weight of an object is represented as the gravitational force acting on an object of mass 'm'. It given by the formula

W = m x g newton

Where,

g - acceleration due to gravity.

Substituting the given values in the above equation

W = 1800 Kg x 9.8 m/s²

= 17640 N

Hence, the weight of the automobile, W = 17640 N

8 0

4 years ago

Which statement accurately describes CI2?

atroni [7]

1. 100,000% A. I simply googled C12 and it's the most stable Isotope of Carbon...

2. A as well.. 99% sure.. and so far my 99% sure has been 100% correct so ... :p

8 0

3 years ago

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