Magnetic Field of a point charge

In summary, a point charge with a charge of -2.9 μC and a velocity of (+7.3 x 105 m/s) k generates a magnetic field at various positions along the z-axis. At position (2.0 cm, 0 cm, 0 cm), the magnetic field is 0 i + (-5.29e-4) j + 0 k. At position (0 cm, 4.0 cm, 0 cm), the magnetic field is (-3.77e-4) i + 0 j + 0 k. At position (0 cm, 0 cm, 1.5 cm), the magnetic field is 0 i + 0 j + 0
  • #1
majormaaz
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1

Homework Statement


A point charge q = -2.9 μC moves along the z-axis with a velocity v = (+7.3 x 105 m/s) k . At the moment it passes the origin, what are the strength and direction of the magnetic field at the following positions? Express each field vector in Cartesian form.

(a) At position r1 = (2.0 cm, 0 cm, 0 cm)
(b) At position r2 = (0 cm, 4.0 cm, 0 cm).
(c) At position r3 = (0 cm, 0 cm 1.5 cm).
(d) At position r4 = (3.5 cm, 1.5 cm, 0 cm).
(e) At position r5 = (3.0 cm, 0 cm, 1.0 cm)

Homework Equations


Bpoint charge = [μ0/4pi] * [qv x sin Θ / r2]

The Attempt at a Solution



I saw that this problem has a negative charge, so I'd have to use the RHR and reverse direction to account for the charge being negative. I also got the fact that the magnetic field at a point along the same axis as the charge's velocity is 0 Teslas.

I ended up with
(a) 0 i + _ j + 0 k
(b) _ i + 0 j + 0 k
(c) 0 i + 0 j + 0 k
(d) _ i + _ j + 0 k
(e) 0 i + _ j + 0 k

However, everytime I used the point charge formula I have, I end up with an incorrect answer. For example, in part (a), with a r = 2 cm = 0.02 m, I plugged that into [μ0/4pi] * [|q|v x sin Θ / r2], and then reversing the sign to account for a negative charge, but it didn't work.
i.e. I calculated that for part (a), a value of 2 cm for r would have a magnetic field of -5.29e-4 T in the j direction, but that's apparently not right.
 
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  • #2
I calculated that for part (a), a value of 2 cm for r would have a magnetic field of -5.29e-4 T in the j direction, but that's apparently not right.
What makes you think that is not right?

$$\vec B = \frac{\mu_0}{4\pi}\frac{q\vec v\times \vec r}{r^3}$$

For part a: ##\vec v = (0,0,v)^t,\;\vec r = (x,0,0)^t##
$$\vec B = \frac{\mu_0q}{4\pi x^3}\left|\begin{matrix}\hat\imath & \hat\jmath & \hat k\\ 0 & 0 & v\\ x & 0 & 0\end{matrix}\right| = \frac{\mu_0 qv}{4\pi x^2}\hat\jmath$$... plug the numbers in and show me your working.

ref: http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html
 

What is a magnetic field?

A magnetic field is a region in space where an electrically charged particle experiences a force due to its motion or spin. It is created by moving electric charges or by the intrinsic magnetic moment of elementary particles.

How is the magnetic field of a point charge calculated?

The magnetic field of a point charge is calculated using the Biot-Savart Law, which states that the magnetic field at a specific point is proportional to the product of the charge, velocity, and the distance from the point charge. It is also affected by the direction of the velocity and the direction of the magnetic field.

What is the direction of the magnetic field of a point charge?

The direction of the magnetic field of a point charge is perpendicular to the plane formed by the velocity and the position vector from the point charge to the point where the field is being calculated. This is known as the right-hand rule.

How does the strength of the magnetic field of a point charge change with distance?

The strength of the magnetic field of a point charge decreases as the distance from the charge increases. This is known as the inverse square law, which states that the strength of a field is inversely proportional to the square of the distance from the source.

Can the magnetic field of a point charge be shielded?

Yes, the magnetic field of a point charge can be shielded using materials with high magnetic permeability, such as iron or steel. These materials redirect the magnetic field lines, reducing the strength of the field outside the shielding material.

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