Use Ampere's Law to solve this question:

**Surface integral (Magnetic field*ds) = ***μ*_{0}** * current**

Current density is J = 2br^5

Plugging in Current density the equation becomes:

**Magnetic field *distance= ***μ*_{0}** * Integral (J*dA)**

**distance= 2pi*r1**

**Magnetic field * (****2pi*r1) = ***μ*_{0 }*** Integral from r1 to 0, (J*2****pi*r dr)**

further more replace J, with 2br^5

**Magnetic field * (****2pi*r1) = ***μ*_{0 }*** Integral from r1 to 0, ((2br^5**)*******2pi*r dr)**

solving the integral we get:

**Magnetic field * (****2pi*r1) = (***μ*_{0 }***4*pi*b *r1^7) /7**

**Magnetic field = ****(***μ*_{0 }***4*pi*b *r1^7) / (7****(****2pi*r1^1))**

**Magnetic field = ****(***μ*_{0 }***2*b *r1^6) / (7****)**

Part B is solved similarly:

**Magnetic field *distance= ***μ*_{0}** * Integral (J*dA)**

**distance= 2pi*r2 (*this is now r2)**

**Magnetic field * (****2pi*r2) = ***μ*_{0 }*** Integral from R to 0, (J*2****pi*r dr)**

plug in J:

**Magnetic field * (****2pi*r2) = ***μ*_{0 }*** Integral from R to 0, (****(2br^5**)***2****pi*r dr)**

solving the integral we get:

**Magnetic field * (****2pi*r2) = (***μ*_{0 }**4pi*b R^7) / 7**** **

**Magnetic field **** = (***μ*_{0 }**4pi*b R^7) / (7**** ***** (****2pi*r2))**

**Magnetic field **** = (***μ*_{0 }**2*b R^7) / (7**** ***** (****r2))**