# Magnetic field formula solenoid

Solenoids are spring-shaped coils of wire commonly used in electromagnets. If you run an electric current through a solenoida magnetic field will be generated.

The magnetic field can exert a force on charged particles that is proportional to its strength. To calculate the force from a solenoid's magnetic field, you can use this equation:. As you can see from the equation, to calculate force we first need to know the magnetic field strength, which is dependent on the characteristics of the solenoid.

We can substitute these parameters into the force equation get:. The calculation looks complicated, but really it's just multiplying a bunch of measurable variables together. Determine the variables in the situation for which you are trying to calculate the force exerted by the magnetic solenoid.

Plug the numbers from your example into the equation and use your calculator to determine the force acting on the charge. If the charge is traveling at anything other than a 90 degree angle to the magnetic field, the whole force equation should be multiplied by the sine of that angle. Timothy Banas has a master's degree in biophysics and was a high school science teacher in Chicago for seven years.

He has since been working as a trading systems analyst, standardized test item developer, and freelance writer. As a freelancer, he has written articles on everything from personal finances to computer technology. Write the equation for the force that a solenoidal electromagnet will exert on a passing charge:.

The solenoidal electromagnet would exert a force of 0. About the Author. Photo Credits.

Copyright Leaf Group Ltd.Picture given below shows the solenoid. A typical solenoid behaves like a bar magnet. Magnetic field produced by solenoid is constant inside the solenoid and parallel to the axis of it. We find the magnetic field produced by solenoid with the following formula.

We find the direction of magnetic field by using right hand rule again. Grab the solenoid as your four fingers shows the direction of current and your thumb shows the direction of magnetic field. Example: Find the magnetic field produced by the solenoid if the number of loop is and current passing through on it is 5 A.

Example: A solenoid has 80 cm diameter, number of loop is 4 and magnetic field inside it is 1,2. Find the current passing through the each loop of wire. Since the questions ask current on each loop, we assume each loop as circle thus we find the magnetic field. Find the magnetic field vector at point A. We sum these vectors using vector properties and get following total magnetic field vector at point A. Magnetism Exams and Solutions.

Tags: calculations of solenoid examples of solenoid magnetic field around a solenoid samples of solenoid. Additional Information.The Biotâ€”Savart law is used for computing the resultant magnetic field B at position r generated by a steady current I for example due to a wire : a continual flow of charges which is constant in time and the charge neither accumulates nor depletes at any point.

The law is a physical example of a line integral: evaluated over the path C the electric currents flow. The equation in SI units is:. Let J be the current density vector, and let d A be a vector that denotes direction and a small differential area.

The direction of d A is normal to the area element. Also parallel to both J and d A is d Lan element of length along the wire. Since the normal to the area is parallel to the length, dAdL equals dV, which is the volume element. Thus the line integral over current becomes a volume integral:. An element of the magnetic field due to an element of current is shown in the figure above and to the right. The rest of solution resembles the calculation of the magnetic field at the center of a loop.

The curve C bounds both a surface Sand any current which pierces that surface is said to be enclosed by the surface. The line integral of the magnetic B-field in teslaT around closed curve C is proportional to the total current I enc passing through a surface S enclosed by C :.

This equation might is not generally valid if a time-dependent electric field is presentas was discovered by James Clerk Maxwell, who added the displacement current term to Ampere's law around The magnetic field is found from Ampere's law :.

This term, the second term on the right, is the displacement current. For applications with no time varying electric fields unchanging charge density it is zero and is ignored. However in applications with time varying fields, such as circuits with capacitors, it is needed, as shown below. So without the displacement current term Ampere's law fails; it gives different results depending on which surface is used, which is inconsistent. Do the line integral around on a circle centered around the loop.

Do the line integral shown. Of the four paths,only l 1 is non-zero. Basic Magnetic Terms definition with Formulas.A long straight coil of wire can be used to generate a nearly uniform magnetic field similar to that of a bar magnet. Such coils, called solenoids, have an enormousnumber of practical applications. The field canbe greatly strengthenedby the addition ofan iron core. Such cores aretypical in electromagnets. The field is essentially perpendicular tothe sides of thepath, giving negligible contribution.

If theend is taken so far from the coil that thefield is negligible, thenthe length inside the coilis the dominant contribution.

### Magnetic flux in solenoid

This admittedly idealized case for Ampere's Law gives. This turns out to be a good approximation for the solenoid field, particularly in the case of an iron core solenoid. At the center of a long solenoid. Enter data, then click on the quantity you wish to calculate in the active formula above the data entry points. Default values will be entered for unspecified parameters, but the numbers will not be forced to be consistent until you click on the quantity to calculate.

Solenoid A long straight coil of wire can be used to generate a nearly uniform magnetic field similar to that of a bar magnet. Derive field expression. Index Magnetic field concepts Currents as magnetic sources. Solenoid Field from Ampere's Law Taking a rectangular path about which to evaluate Ampere's Law such that the length of the side parallel to the solenoid field is L gives a contribution BL inside the coil.

This admittedly idealized case for Ampere's Law gives This turns out to be a good approximation for the solenoid field, particularly in the case of an iron core solenoid. Solenoid Magnetic Field Calculation At the center of a long solenoid. Active formula: click on the quantity you wish to calculate.Consider a long solenoid having n number of turns per unit length and carrying current I is as shown in figure.

The magnetic field outside the solenoid is almost zero but the magnetic field inside the solenoid is uniform which is directed along the axis of the solenoid.

If dl be the small line element the direction of B is along dl. If N be the no. Velocity of Sound in Laplace Correction Physical Factors Affecting of Vibration in the stretched Characteristics of Musical Sound. Laws of refraction of Interference Super position principle Interference of light Analytical treatment of interference Maximum and minimum Intensity Diffraction Diffraction Fraunhofer diffraction at single Diffraction grating Short Question. Velocity of Light by Combination of Resistors Alternating current AC.

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## Solenoids and Magnetic Fields

Magnetic field Orested Discovery Magnetic field lines and Force on moving charge Force on Current carrying Torque on rectangular coil Moving coil Galvanometer Biot-Savart Law. Application of Biot-Savart Law Magnetic field along the Magnetic field at the Magnetic Field due to Magnetic field along axis Magnetic field due to Magnetic properties of materials. Electromagnetic Induction. Alternating Currents Mean value or average Root mean square value AC through resistor and AC through inductor, capacitor AC through resistor, capacitorA solenoid is a coil of wire designed to create a strong magnetic field inside the coil.

By wrapping the same wire many times around a cylinder, the magnetic field due to the wires can become quite strong. The number of turns N refers to the number of loops the solenoid has. More loops will bring about a stronger magnetic field.

The formula for the field inside the solenoid is. The blue crosses represent the current traveling into the page, while the blue dots represent the currents coming out of the page. Ampere's law left for the red path can be written as. Only the upper portion of the path contributed to the sum because the magnetic field is zero outside, and because the vertical paths are perpendicular to the magnetic field.

By dividing x out of both sides of the last equation, one finds:. The magnetic field inside a solenoid is proportional to both the applied current and the number of turns per unit length. There is no dependence on the diameter of the solenoid, and the field strength doesn't depend on the position inside the solenoid, i.When electric current is carried in a wire, a magnetic field is formed around it.

The magnetic field lines form concentric circles around the wire. The magnetic field direction depends on the direction of the current. It can be determined using the "right hand rule", by pointing the thumb of your right hand in the direction of the current. The direction of the magnetic field lines is the direction of your curled fingers. The magnitude of the magnetic field depends on the amount of current, and the distance from the charge-carrying wire.

The formula includes the constant. This is called the permeability of free space, and has a value. The unit of magnetic field is the Tesla, T. If the current has a vector direction out of the page or screenwhat is the direction of the magnetic field? Answer: The magnitude of the magnetic field can be calculated using the formula:.

Magnetic Fields Inside Solenoids

The magnitude of the magnetic field is 6. The direction of the magnetic field can be determined using the "right hand rule", by pointing the thumb of your right hand in the direction of the current. The current has a vector direction out of the page, and so your fingers will curl in the counter-clockwise direction.

Therefore, the magnetic field lines point in the counter-clockwise direction, forming circles around the wire. If the magnetic field lines form clockwise circles in the plane of the page or screenwhat is the vector direction of the electric current?

Answer: The magnitude of the electric current can be calculated by rearranging the magnetic field formula:. The magnitude of the magnetic field is given in nano-Tesla. The prefix "nano" means 10 -9and so. The magnitude of the magnetic field at the distance specified is thus:. The direction of the electric current can be determined using the "right hand rule". The magnetic field lines form clockwise circles in the plane of the page, so imagine curling your right hand so that your fingers point in the clockwise direction.

To do this, your thumb must point toward the page or screen. Therefore, the direction of the electric current is into the page or screen.

Toggle navigation. Magnetic Field Formula When electric current is carried in a wire, a magnetic field is formed around it. Magnetic Field Formula Questions: 1 What is the magnitude of the magnetic field 0. Answer: The magnitude of the magnetic field can be calculated using the formula: The magnitude of the magnetic field is 6.

Answer: The magnitude of the electric current can be calculated by rearranging the magnetic field formula: The magnitude of the magnetic field is given in nano-Tesla.