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# A Isaev

• ### Magnetic flux through a coil?

I've already maxed out my attempts for this question, but I want to know the answer anyway.

The question refers to the following situation of two coils, one connected to a power supply and the other to a voltmeter.

The current in coil 1 is varying due to the power supply. At time t = 0 s it is I0 = 18 A and at t = 0.4 s it is I0.4 = 6 A. The conventional current in the top wire points from the power supply to the coil (i.e. from left to right)

The parameters of the system are as follows. Coil 1 has N1 = 588 turns of wire and its radius is R1 = 0.05 m. Coil 2 has N2 = 275 turns of wire and its radius is R2 = 0.03 m. The distance between the centres of the coils is d = 0.14 m.

At time t = 0 s what is the magnetic flux through one turn of coil 2? Answer in units of μT m2.

Remember that all turns of coil 1 contribute to the magnetic field.

Thanks :)

• ### magnetic force and a flashlight battery?

(a) If a flashlight battery (1.5 V) has an internal resistance of 0.2 ohm, and a bar magnet produces a magnetic field of about 0.500 tesla near the end of the magnet, what is the approximate magnetic force on w = 7 centimeters of a wire that short-circuits the battery? Assume +x is to the right, +y is up, and +z is out.

(b) Suppose you turn the bar magnet upside down so that the south pole is up. What is the magnetic force now?

• ### magnetic field and an electron?

A long straight wire suspended in the air carries a conventional current of 6.7 amperes in the -x direction (the wire runs along the x-axis). At a particular instant an electron at location < 0, -0.003, 0 > m has velocity < -2.5*10*5, -3*10^5, 0 >m/s

(a) What is the magnetic field due to the wire at the location of the electron?

(b) What is the magnetic force on the electron due to the current in the wire?

(c) If the moving particle were a proton instead of an electron, what would the magnetic force on the proton be?

• ### magnetic field due to an electron?

A long straight wire suspended in the air carries a conventional current of 6.7 amperes in the -x direction (the wire runs along the x-axis). At a particular instant an electron at location < 0, -0.003, 0 > m has velocity < -2.5 * 10^5, -3 *10^5, 0 >m/s.

(a) What is the magnetic field due to the wire at the location of the electron?

any help appreciated.

• ### Invertible linear tranformations - uni maths.?

Consider the linear transformation

T (x1 , x2 , x3 , x4 , x5 ) = (x1 + 2x2 + 3x3 + 4x4 + 5x5 , 6x1 + 7x2 + 8x3 + 9x4 + 10x5 ,

2x3 + 2x4 + 3x5 , 4x3 + 5x4 + 6x5 , 7x3 + 8x4 + 9x5 ).

Show that T is invertible, that is, there exists a linear transformation S : R5 → R5 (called

the inverse of T ), such that S (T (x)) = T (S (x)) = x for every x in R5 . Find the standard

matrix of the inverse of T . Show all the calculations.

Any help appreciated. :)

• ### mean value theorem - uni maths?

Prove that lim x →0 (sin x)/x = 1.

Notes: (i) You may use any standard properties of the trigonometric functions, includ-

ing the formulas for their derivatives.

(ii) This formula is used to prove that the derivative of sin is cos, so it is usually proved

by other methods.

Any help appreciated.

• ### Potential along different paths in a capacitor - physics?

A capacitor consists of two charged disks of radius 3.5 m separated by a distance s = 2 mm. The magnitude of the charge on each disk is 37 µC. Consider points A, B, C, and D

[b a]

[c d]

inside the capacitor. The distance between B and A is1.6 mm, and the distance between B and C is 0.8 mm.

Find Vb - Va and Vc - Vb, then determine Vc - Va.

Any help would be appreciated as I am really stuck on this question.

Thanks.

• ### Matrix Algebra - University Maths?

I have no idea how to approach this question and my textbook is less than useful, so I'd appreciate any help especially if you can show step by step what you're doing.

Suppose that A is a square matrix of size n x n that satisfies the matrix equation:

A^14 A^T A^14 + 72A^5 (A^T)^2 A^5 + 16A A^T A^3 - 7I = 0

Show that the matrix is invertible and find an expression for A^-1 in terms of A.

Thanks.

• ### differentiability - university maths?

Suppose g is continuous in (-1, 1) and diferentiable in (-1, 0) U (0, 1)

Use the mean value theorem to prove that if lim(x->0+) g'(x) = lim(x->0-) g'(x)

with both limits finite, then g is differentiable at 0.

Any help appreciated :)

• ### differentiability - uni maths?

let f(x) =

{(x^2) sin(1/x) x=/=0

0, x=0}

Show that f'(x) exists at every x, but f' is not continuous at x=0

Any help appreciated :)

• ### Matrix Algebra - University Maths?

Alright, I have a problem with one question. I can see how it works in my head, but I just don't know how to show it.

Let A be an m x n matrix and B be an n x p matrix. Show that if the columns of B are linearly dependent, the so are the columns of AB.

Any help appreciated :)

• ### Matrix Algebra - University Maths?

Let the 2 x 2 matrix A =

[5 -35]

[-1 7]

Construct a 2 x 4 matrix B with pairwise distinct non-zero columns such that AB=0.

Also construct a 3 x 2 matrix C with pairwise distinct non-zero rows such that CA=0.

Any help would be appreciated. Thanks.

• ### Is the function f(x) = x^3 + x uniformly continuous on R?

Hi Guys, A little help with this would be appreciated.

Is the function f(x) = x^3 + x uniformly continuous on R? Prove your answer.

I don't think it is - but I don't really know how to solve it.

Thanks.

• ### Intermediate Value Theorem - University Maths?

I struggling a little bit with this question. Any help would be appreciated.

Suppose that f is continuous of [a,b] and f takes only rational values. What can be concluded about f?

• ### Continuity - University Maths?

Hi guys,

I can't work out a question in my homework - any help would be appreciated, I'm really stuck.

Prove that the function f defined by:

f(x) = {0, x is irrational}

{1/q, x = p/q is rational in lowest terms}

is continuous at every irrational and discontinuous at every rational.

Thanks.

• ### Physics: one mole of copper etc?

One mole of copper (6 1023 atoms) has a mass of 64 grams, and its density is 8.95 grams per cubic centimeter. You have a long thin bar of copper, 2.1 m long, with a square cross section, 0.15 cm on a side.

You hang the rod vertically and attach a 139 kg mass to the bottom, and you observe that the bar becomes 1.06 cm longer. Calculate the effective stiffness of the interatomic bond, modeled as a "spring":

Next you remove the 139 kg mass, place the rod horizontally, and strike one end with a hammer. How much time t will elapse before a microphone at the other end of the bar will detect a disturbance?

Any help would be greatly appreciated :)

Thanks

• ### Physics, Spring length?

A ball of mass 580 g hangs from a spring whose stiffness is 190 newtons per meter. A string is attached to the ball and you are pulling the string to the right, so that the ball hangs motionless, as shown in the figure. In this situation the spring is stretched, and its length is 15 cm.

What would be the relaxed length of the spring, if it were detached from the ball and laid on a table?

I can put the picture here, but it shows the spring being pulled to the right of the normal with a distance of 8cm. Using simple trigonometry I found that the angle between the spring and the normal was 32.231 degrees if that helps.

Any help would be greatly appreciated.

Thanks.

• ### Buoyant force formula?

Calculate the buoyant force in air on a kilogram of lead (whose density is about 11 grams per cubic centimeter). The density of air is 1.3 10-3 grams per cubic centimeter. Remember that the buoyant force is equal to the weight of a volume of air that is equal to the volume of the object. (Compare with the weight mg of this much lead, which is 9.8 N.)

What formula should I use for this? I looked in the text book - but it didn't seem to help. I tried a few didfferent things, but nothing seemed to work. I'm more interested in knowing how to work this out than the answer and any help would be appreciated.

• ### Momentum and force on the z component?

At a certain instant the z component of the momentum of an object is changing at a rate of 9 kg · m/s per second. At that instant, what is the z component of the net force on the object?

I'm not sure if there is enough information to be able to solve this? Can someone please tell me how!

Thanks.