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Compute the curl of the vector field.

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Final answer:

The question pertains to the calculation of the curl of a vector field, a concept in vector calculus used to measure a field's rotation. Additionally, vector algebra and the Lorentz force in physics are also discussed.

Step-by-step explanation:

The task is to compute the curl of a vector field, which is a concept in vector calculus, particularly in the fields of multivariable calculus and differential geometry. The curl measures the rotation of the field at a particular point and is represented by a vector.

To do so, typically one has to apply the curl operator (∇ ×) to the given vector field using partial derivatives. An example, if a vector field is given by F = P + Q + Rk, the curl of F would be:

Curl F = (∂R/∂y - ∂Q/∂z) + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k.

For vector algebra, solving equations involving vectors usually requires knowledge of linear algebra and concepts such as vector addition and scalar multiplication. In the given equation 2à – 6B + 3ℓ = 2ℓ, it is needed to first define the vectors à and B and then solve for vector ℓ.

For the physics application involving magnetic fields and currents, the key formula to remember is Lorentz's force, which is F = q(v × B), where q is the charge, v is the velocity vector, and B is the magnetic field vector.

User Joshua Zollinger
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