# Find the equation of this magnetic field

• Istiak
In summary, the question asks you to find the magnetic field of an electron that enters a square region ABCD with area a. You are asked to find the minimum magnetic field strength that will cause the electron to exit the square in the direction opposite from the direction it was fired in.
Istiak
Homework Statement
An electron with velocity v =##2 \times 10^6 \\ \mathrm {ms^-1}##
enters a square region ABCD (of area a = ##1 \\ \mathrm cm^2##
along one of its side AB. Inside the region there is a magnetic field B perpendicular to the
area of the square. Find the minimum value of magnetic field for which the electron will
come out of the square with a velocity parallel to its initial velocity(parallel doesn't
necessarily mean in the same direction).
Relevant Equations
##\vec B = \frac{\mu_0 q \vec v\times \hat r}{4\pi r^2}##
When I try following numbers from internet then I don't get an expected answer.

## \mu_0 = 1.25663706 × 10-6 m kg s^{-2} A^{-2}##
##q =1.60217662 × 10^{-19} coulombs ##
##r=2.82x10^{-15} m##
Velocity of that electron is given in question

##\vec v= 2 \times 10^6 \\ \mathrm{ms^{-1}}##Since magnetic field is perpendicular to the surface that's why I took ##\vec v \times \hat r=||v||## Wait a minute, Magnetic field is perpendicular but not velocity and velocity is parallel so ##\vec v \times \hat r=0##. But if I tried it then I would get "nothing". Did I take wrong equation? Or there's some concept which I haven't figured out?

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Where did you get the value of ##r## from?

Edit: Also, why do you think the field is given by that formula?

Orodruin said:
Where did you get the value of ##r## from?
That appears to be the radius of an electron!

Orodruin said:
Where did you get the value of ##r## from?

Edit: Also, why do you think the field is given by that formula?
I found the ##r## from internet where it is, radius of an electron. I found that equation in a book so I believe magnetic field is given by that equation. But I worry I can't derive one for a square.

##\oint \vec B \cdot d\vec l = \mu_0 I_{enc}##
##\vec B =\frac{\mu_0 I_{enc}}{2r}##

My given equation was from (steady current law)
##\vec B = \frac{\mu_0 }{4\pi}\int\frac{\vec K \times \hat r}{r^2}da\prime##
##=\text{given at top of the thread.}##

Istiakshovon said:
I found the ##r## from internet where it is, radius of an electron. I found that equation in a book so I believe magnetic field is given by that equation. But I worry I can't derive one for a square.

##\oint \vec B \cdot d\vec l = \mu_0 I_{enc}##
##\vec B =\frac{\mu_0 I_{enc}}{2r}##

My given equation was from (steady current law)
##\vec B = \frac{\mu_0 }{4\pi}\int\frac{\vec K \times \hat r}{r^2}da\prime##
##=\text{given at top of the thread.}##
Does the question ask you to find the magnetic field of an electron?

PeroK said:
Does the question ask you to find the magnetic field of an electron?
An electron with velocity v =##2 \times 10^6 \\ \mathrm {ms^-1}##
enters a square region ABCD (of area a = ##1 \\ \mathrm cm^2##
along one of its side AB. Inside the region there is a magnetic field B perpendicular to the
area of the square. **Find the minimum value of magnetic field** for which the electron will
come out of the square with a velocity parallel to its initial velocity(parallel doesn't
necessarily mean in the same direction).

Take a look at what I bold...!

Istiakshovon said:
Find the minimum value of magnetic field for which the electron will
come out of the square with a velocity parallel to its initial velocity(parallel doesn't
necessarily mean in the same direction).
IMO, it would be better if the question stated simply what it wants you to find. You are aked to calculate the minimum strength of the magnetic field so that the electron exits the square in the direction opposite from the direction it was fired in.

To do the problem you must know or calculate the shape of the trajectory of a charged particle in a uniform magnetic field.

## 1. What is a magnetic field equation?

A magnetic field equation is a mathematical representation that describes the behavior of a magnetic field. It includes variables such as the strength and direction of the field, as well as the position of the magnetic source.

## 2. How do you find the equation of a magnetic field?

To find the equation of a magnetic field, you need to know the properties and position of the magnetic source, as well as the properties of the surrounding medium. You can then use mathematical formulas, such as the Biot-Savart Law or Ampere's Law, to calculate the strength and direction of the magnetic field at different points.

## 3. What are the units of a magnetic field equation?

The units of a magnetic field equation depend on the specific equation being used. In general, magnetic field strength is measured in units of tesla (T) or gauss (G), while distance is measured in meters (m) or centimeters (cm).

## 4. How accurate are magnetic field equations?

Magnetic field equations are based on mathematical models and assumptions, so their accuracy depends on the accuracy of these assumptions and the precision of the measurements used to calculate them. In general, they can provide a good estimate of the behavior of a magnetic field, but may not be completely accurate in all situations.

## 5. Can magnetic field equations be used for all types of magnetic fields?

No, magnetic field equations are specific to different types of magnetic fields, such as those produced by a current-carrying wire or a permanent magnet. It is important to use the appropriate equation for the specific type of magnetic field being studied.

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