Question

unit of magnetic field
$\beta$
​

Answer 1

Explanation:

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Answer 2

Answer:

Explanation:

magnetic field will apply a force on a single moving charge, and it will also exert a force on a current on which is a collection of moving charges. The force encountered by a wire of length l carrying a current I in a magnetic field B is expressed by.

F = I L B sin Theta

The Force on a Current in a Magnetic Field-1.gif

The magnetic force on a current-carrying wire is perpendicular to the wire and the magnetic field with location given by the right hand rule.

The Force on a Current in a Magnetic Field-2.gif

If the angle between the current and magnetic field $B$; $B=0$ then $sinbeta=0$, $F=0$, $beta=180$ then $sinbeta=0$, $F=0$, $beta=90$ then $sinbeta=1$, $F=B.i.l$. Therefore, if the direction of current and magnetic field are parallel to each other then, no force exerted on the wire.

The Force on a Current in a Magnetic Field-3.png

Force Acting on Charged Particle

Force acting on a current was explained above. Current is produced by the movements of charged particles. Therefore, force on current carrying wire is the total of forces acting on each charged particle which this current. If the particle has charge q, velocity v and it is positioned in a magnetic field having strength B force acting on this particle and beta is the angle between the velocity and magnetic field is found with the formula.: $F = q.v.B.sinbeta$.

The Force on a Current in a Magnetic Field-4.png

Conditions occur:

1. if $v = 0$, then $F=0$ no force exerted on stationary particle in magnetic field.

2. if $beta=0$, then $sin0=0$ and $F=0$.

3. if $beta=180$, then $sin180=0$, and $F=0$, magnetic field lines and velocity of particle parallel to each other, then no force exerted on it.

4. if $beta=90$, then $sin90=1$, $F=q.v.B$.

vConditions occur:

1. if v = 0, then F=0 no force exerted on stationary particle in magnetic field.

2. if beta=0, then sin0=0 and F=0

3. if beta=180, then sin180=0, and F=0, magnetic field lines and velocity of particle parallel to each other, then no force exerted on it.

4. if beta=90, then sin90=1, F=q.v.B

Forces of Currents Carrying Wires on Each Other

It shows that currents in the same direction attract each other since they create opposite magnetic fields. On the other hand, currents in opposite directions repel each other since they produce magnetic fields having same directions. Using the formula, we can find the force exerted on each of them.

The Force on a Current in a Magnetic Field-5.png

$F = B_1i_2I=2kfrac{i_1i_2}{d}I$

wherein $l$ is the length of the wires and $d$ is the distance between them.

Sample Problem:

Find the directions of the magnetic forces acting on the currents $I_1$, if $I_2$ is placed in a constant magnetic field.

The Force on a Current in a Magnetic Field-6.png

Solution:

By following the right hand rule, therefore, the answer is shown i below;

The Force on a Current in a Magnetic Field-7.png

The Hall Effect

One good application of the force exerted by moving charges is the Hall effect. It is also a common way of measuring the strength of a magnetic field. A buildup of charge at the sides of a thin flat conductor will balance this magnetic influence, producing a measurable voltage between the two sides of the conductor. The presence of this measurable transverse voltage is called the Hall effect.

The Hall coefficient is stated as the ratio of the induced electric field to the product of the current density and the magnetic field. It has a feature of the material from which the conductor is made, its value depends on the type, number, and properties of the charge carriers that comprise the current.

The Force on a Current in a Magnetic Field-8