Question

H=rhozcosϕaₚ +e−² sin
ϕ/2 aϕ+rho²azGiven the vector field at point (1,π/3,0), find
H⋅aₓ

Answer 1

To find H⋅aₓ at the given point, we substitute the given values into the vector field equation and calculate the dot product.

Step-by-step explanation:

To find H⋅aₓ at the given point (1,π/3,0), we substitute the given values into the vector field equation and calculate the dot product.

H = ρzcosϕaₚ + e^(-² sin(ϕ/2))aϕ+ρ²az

• ρ = 1
• z = 0
• ϕ = π/3

Substituting these values in, we get:

H = (1)(0)cos(π/3)aₚ + e^(-² sin(π/6/2))aϕ+(1)²az

Simplifying further, we have:

H = 0*aₚ + e^(-²*sin(π/12))aϕ + az

Finally, to find the dot product, we multiply the corresponding components:

H⋅aₓ = (0)(aₓ) + (e^(-²*sin(π/12)))(0) + (1)(0) = 0