A proton moves perpendicularly to a uniform magnetic field, 𝐁, with a speed of 1.0 ×10^7 m / s a

A proton moves perpendicularly to a uniform magnetic field,...

A proton moves perpendicularly to a uniform magnetic field, $\mathbf{B}$, with a speed of $1.0 \times 10^{7} \mathrm{m} / \mathrm{s}$ and experiences an acceleration of $2.0 \times 10^{13} \mathrm{m} / \mathrm{s}^{2}$ in the positive $x$ direction when its velocity is in the positive $z$ direction. Determine the magnitude and direction of the field.

Key Concepts

Uniform Magnetic Field

A uniform magnetic field is one in which the strength and direction of the field remain constant at all points. This uniformity simplifies the analysis of charged particle motion, leading to predictable trajectories such as circular motion when the velocity is perpendicular to the field.

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in electromagnetic fields. It is given by the cross product between the velocity of the particle and the magnetic field, meaning the force is perpendicular to both. This concept is essential in understanding how magnetic fields influence the motion of charged particles without doing work on them.

Charged Particle Motion in a Magnetic Field

When a charged particle enters a region with a uniform magnetic field, it experiences a magnetic force that can cause it to move in a circular or helical path if its velocity is not aligned with the field. The magnetic force provides the centripetal force necessary for circular motion, and its magnitude depends on the charge, speed, and magnetic field strength.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the force on a positive charged particle moving in a magnetic field. By aligning the thumb with the velocity vector and the fingers with the magnetic field, the resulting direction in which the palm pushes corresponds to the force's direction.

Transcript

00:01 Hello guys, so the question states a proton moves perpendicular to a uniform magnetic field b with the speed of 1 .0 times 10x to power 7, 1 .0 times 3 per 7 meter per second, an expression on acceleration of 2 .0 times 10 per 30 meter per second square in a positive x direction in a positive x direction when its velocity is in a positive z direction.

00:38 Determine the magnitude and direction of the field.

00:45 Also, speed.

00:53 From speed is given us 1 .0 times 10 reciprocal 7.

01:18 1 .0 times 9 .7 meter per second.

01:29 And acceleration which i would just call a was given us 2 .0 times multiplied by 10 reciprocal meter per second square in the positive x direction when its velocity is is in the positive z direction.

02:20 So this is a speed and acceleration of the proton.

02:31 This is a speed and acceleration of the proton.

02:57 And it's telling us to calculate the magnitude of the field and also the direction.

03:03 And the magnitude of a field is calculated using f is equal to to quay, q, sorry, v multiplied by b.

03:34 With b standing for the magnitude of the field.

03:37 So on b is made the subjector formula.

03:42 So b is equal to f divided by q multiplied by v.

03:59 But from the given values it is quite vague to know the force of the proton.

04:06 And the chart of the proton as well.

04:14 For using our standardized knowledge of the values given of a proton, we can state for the fact that the mass of a proton is 1 .67...

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