The direction of the magnetic force on a relocating positively charged fragment or a cable carrying current $i$ in a uniform magnetic field is determined by the right-hand rules with different versions stated below.

Version 1 (right-hand rule): point the finger of your appropriate hand in the direction of $\vec v$ and also curl castle (through the smaller sized angle) towards $\vec B$. Your upright thumb reflects the cross product $\vec v \times \vec B$ or the magnetic pressure $\vec F_B$. This force is perpendicular come the airplane of $\vec v-\vec B$

Version 2 (right-hand rule): point your fingers in the direction that $\vec B$ so the the thumb points toward the velocity $\vec v$, her palm shows the direction the the magnetic force on a hopeful charge.

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Note: the magnetic force on a an unfavorable charge is in the contrary direction come that given by the right-hand rule.

## Right-Hand Rule: instance problems

Example (1): What is the direction that the magnetic field that produce the magnetic force on a confident charge in every of the numbers below. (assuming $B$ is perpendicular come $v$).

Solution: right-hand dominance states that, to recognize the direction of the magnetic force on a positively fee particle, allude the thumb of the right hand in the direction of $v$, the fingers in the direction of $B$, and also your palm in the direction that magnetic force $F$. Therefore, in the following figure we have

Where $\odot$ and $\otimes$ show the direction the the fields as outward and inward, respectively, perpendicular to the page.

Example (2): What is the direction the the magnetic force on a negative charge beginning a uniform magnetic field B in the complying with figure.

Solution: placed your ideal fingers in addition to the velocity such the your palm reflects the direction that the magnetic ar B. In this situation, your thumb, the direction that the magnetic force, goes into the page.

But note that this force is for a optimistic charge. Because that a negatively charged particle, simply reverse the above direction that is the end of the page.

Example (3): making use of the right-hand rule, find the direction of the magnetic force on the positively charged fragment in the figure below.

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Solution: location your right hand on the plane, such the your finger directed along with the velocity V and the palm come the magnetic field. Your thumb mirrors the direction of the magnetic force on the positive charge. This is the right-hand rule.

In this problem, the ignorance is toward the right.

Example (4): Repeat the problem over with a an unfavorable charge.

Solution: together a rule of thumb, to uncover the direction that the magnetic pressure on a negatively fee particle, an initial always expect the fee is positive, find the force's direction on it then turning back its direction to uncover the force's direction top top the corresponding an adverse charge.

Hence, in this problem, the force is directed towards the left.

Example (5): making use of the right-hand rule, uncover the direction the the velocity in the adhering to figure.

Solution: Recall the in the right-hand rule, each component that the appropriate hand represents something.

The fingers show the direction of the particle's velocityThe ignorance is because that the direction of the magnetic force. The palm reflects the direction of the magnetic field.

Put your best hand ~ above the web page in the order explained above. By act this, her palm is encountering up. Thus, the particle's velocity is out of the page.

Example (6): an steady existing passes v the wires in addition to a lengthy solenoid and produces a uniform magnetic field parallel to its axis. A confident charge relocating along the axis the the solenoid enters right into it. In what direction is the magnetic force applied to the charge?

Solution: Recall the the magnetic pressure on a charged bit is obtained by $F=q\vecv\times \vecB=qvB\sin \theta$ wherein $\theta$ is the angle in between the particle's velocity and the magnetic field.

Here, this angle is zero since both the velocity and also magnetic field are in the very same direction.

Hence, no magnetic force is used to the particle.

Example (7): a negatively charged particle, moving to the appropriate along a horizontal plane, is entering into a an ar of uniform magnetic ar directed into the page. In what direction is the magnetic force?

Solution: First, visualize what is being claimed in the following figure.

Now apply the right-hand rule: your appropriate fingers along with the velocity so that the palm is in the direction that the magnetic field. The thumb, which shows the force's direction, is upward.