You are watching: Consider the magnetic fields and velocities of charged particles shown in the figure

What is the device by which one magnet exerts a pressure on another? The answer is related to the fact that all magnetism is caused by present, the flow of charge. *Magnetic fields exert forces on relocating charges*, and also so they exert pressures on other magnets, all of which have moving charges.

The magnetic force on a relocating charge is among the a lot of basic well-known. Magnetic force is as crucial as the electrostatic or Coulomb pressure. Yet the magnetic force is even more facility, in both the number of factors that affects it and also in its direction, than the relatively basic Coulomb pressure. The magnitude of the * magnetic force **F* on a charge *q* moving at a speed *v* in a magnetic field of strength *B* is given by

*F *= *qvB* sin *θ*,

wbelow *θ* is the angle in between the directions of v and also B. This force is often dubbed the * Lorentz force*. In fact, this is exactly how we specify the magnetic field toughness *B*—in terms of the force on a charged pwrite-up relocating in a magnetic area. The SI unit for magnetic area toughness *B* is called the * tesla* (T) after the eccentric however brilliant inventor Nikola Tesla (1856–1943). To determine exactly how the tesla relates to other SI devices, we solve *F *= *qvB* sin *θ* for *B*.

Because sin *θ* is unitmuch less, the tesla is

(note that C/s = A). Anvarious other smaller sized unit, referred to as the * gauss* (G), where 1 G = 10−4 T, is periodically supplied. The strongest irreversible magnets have fields near 2 T; superconducting electromagnets might achieve 10 T or even more. The Earth’s magnetic field on its surface is only about 5 × 10−5 T, or 0.5 G.

The *direction* of the magnetic pressure **F** is perpendicular to the aircraft created by **v** and **B**, as determined by the * ideal hand preeminence 1* (or **RHR-1**), which is shown in Figure 1. RHR-1 says that, to identify the direction of the magnetic pressure on a positive moving charge, you point the thumb of the ideal hand in the direction of **v**, the fingers in the direction of **B**, and also a perpendicular to the palm points in the direction of **F**. One method to remember this is that there is one velocity, and also so the thumb represents it. There are many kind of field lines, and also so the fingers reexisting them. The pressure is in the direction you would push through your palm. The force on an adverse charge is in exactly the oppowebsite direction to that on a positive charge.

Figure 1. Magnetic fields exert pressures on relocating charges. This force is among the many standard known. The direction of the magnetic force on a moving charge is perpendicular to the airplane developed by v and B and also follows best hand rule–1 (RHR-1) as displayed. The magnitude of the pressure is proportional to q, v, B, and also the sine of the angle in between v and B.

With the exemption of compasses, you seldom see or personally experience pressures due to the Earth’s small magnetic field. To show this, expect that in a physics lab you rub a glass rod through silk, placing a 20-nC positive charge on it. Calculate the force on the rod due to the Earth’s magnetic area, if you throw it with a horizontal velocity of 10 m/s due west in a location wright here the Earth’s area is due north parallel to the ground. (The direction of the pressure is figured out via ideal hand dominion 1 as presented in Figure 2.)

Figure 2. A positively charged object relocating due west in an area wbelow the Earth’s magnetic field is due north experiences a pressure that is straight dvery own as shown. A negative charge relocating in the same direction would certainly feel a pressure directly up.

**Strategy**

We are given the charge, its velocity, and also the magnetic field stamina and also direction. We can for this reason use the equation *F *= *qvB* sin *θ* to discover the pressure.

**Solution**

The magnetic pressure is

*F *= *qvB* sin *θ*

We watch that sin *θ = *1, given that the angle in between the velocity and the direction of the field is 90º. Entering the various other given quantities yields

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**Discussion**

This pressure is totally negligible on any type of macroscopic object, regular with endure. (It is calculated to just one digit, given that the Earth’s area varies via area and is provided to only one digit.) The Earth’s magnetic field, however, does produce exceptionally essential impacts, particularly on submicroscopic particles. Some of these are explored in Force on a Moving Charge in a Magnetic Field: Examples and also Applications.