Help Help Needed huhu Physics Problem

[michigan_king]

 

[Raging_Jalapeno]

Pwede pa copy paste ng problem paps, sunod pagnagtanong ka po kun pwede wag naka-image yung question

To determine the magnitude and direction of the magnetic field produced by the negative charge q at different points, we can use the Biot-Savart Law, which gives the magnetic field at a point P due to a current element dl carrying current I:

d𝐵 = (μ₀/4π) (𝐼 dl × 𝐫) / r²

where 𝐼 is the current, dl is an element of the current path, 𝐫 is the vector from the element dl to the point P, r is the distance between dl and P, and μ₀ is the permeability of free space (μ₀ = 4π × 10^-7 T m/A).

For a point charge moving with a velocity v, the current element can be expressed as I = qv, where q is the charge and v is the velocity. Therefore, we can write the magnetic field at a point P due to a point charge q with velocity v as:

𝐵 = (μ₀/4π) (q𝐯 × 𝐫) / r²

where 𝐯 is the velocity of the charge.

Let's now use this formula to calculate the magnetic field at the specified points.

At point A = (0.200 m) î + (0.150 m) ĵ + (0.300 m) k:
The distance from the charge q to point A is:

r = |𝐫| = √(0.200² + 0.150² + 0.300²) = 0.374 m

The vector from the charge q to point A is:

𝐫 = A - 𝐫q = (0.200 m) î + (0.150 m) ĵ + (0.300 m) k

where 𝐫q = 0 î + 0 ĵ + 0 k is the position vector of the charge q at the origin.

The magnetic field at point A is then:

𝐁 = (μ₀/4π) (q𝐯 × 𝐫) / r²

𝐁 = (4π × 10^-7 T m/A) (-(3.60 × 10^-6 C)(7.50 × 10^4 m/s) î + (3.60 × 10^-6 C)(4.90 × 10^4 m/s) ĵ) / 0.374²

𝐁 = (-0.225 T) î + (0.367 T) ĵ

The magnitude of the magnetic field at point A is:

|𝐁| = √(0.225² + 0.367²) = 0.433 T

The direction of the magnetic field at point A is:

θ = tan⁻¹(𝐁/|𝐁|) = tan⁻¹(0.367/-0.225) = -59.4°

Therefore, the magnitude of the magnetic field at point A is 0.433 T, and its direction is 59.4° below the negative x-axis.

At point B = (0.300 m) î + (0.100 m) ĵ - (0.400 m) k:
The distance from the charge q to point B is:

r = |𝐫| = √(0.300² + 0.100² + 0.400²) = 0.488 m

The vector from the charge q to point B is:

𝐫 = B - 𝐫q = (0.300 m) î + (0.100 m)

 

[michigan_king]

Raging_Jalapeno noted po, thank you lodsss

ay iba pala mga given sa solution kaya iba mga sagot anyway, salamat pa rin