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As the other answers already pointed out, there's no such spheric region. The field produced by the magnetic dipole will be given by $$\mathbf{B}_d(r,\theta)=\frac{\mu_0m_0}{4\pi}\frac{3\hat{\mathbf{r}}\cos\theta-\hat{\mathbf{z}}}{r^3}$$ So, adding both fields, we cannot make it null for a fixed $r$, since the component on the $z$ direction will be constant but the radial is $\theta$ dependent. What can be made, as @mcodesmart posted is to get a zero flux on a sphere. In this case, the radial field will be zero. For this we must have $$\frac{\mu_0m_0}{4\pi}\frac{3\cos\theta-\cos\theta}{r^3}+B_0\cos \theta=0\implies\\ r=\left(-\frac{\mu_0m_0}{2\pi B_0}\right)^{1/3}$$ which shows that the uniform field must be oriented in the opposite sense of the dipole.

As the other answers already pointed out, there's no such spheric region. The field produced by the magnetic dipole will be given by $$\mathbf{B}_d(r,\theta)=\frac{\mu_0m_0}{4\pi}\frac{3\hat{\mathbf{r}}\cos\theta-\hat{\mathbf{z}}}{r^3}$$ So, adding both fields, we cannot make it null for a whole spherical surface, which in spherical coordinates means fixed $r$, since the component on the $z$ direction will be constant but the radial is $\theta$ dependent. What can be made, as @mcodesmart posted is to get a zero flux on a sphere. In this case, the radial field will be zero. For this we must have $$\frac{\mu_0m_0}{4\pi}\frac{3\cos\theta-\cos\theta}{r^3}+B_0\cos \theta=0\implies\\ r=\left(-\frac{\mu_0m_0}{2\pi B_0}\right)^{1/3}$$ which shows that the uniform field must be oriented in the opposite sense of the dipole.

As the other answers already pointed out, there's no such spheric region. The field produced by the magnetic dipole will be given by $$\mathbf{B}_d(r,\theta)=\frac{\mu_0m_0}{4\pi}\frac{3\hat{\mathbf{r}}\cos\theta-\hat{\mathbf{z}}}{r^3}$$ So, adding both fields, we cannot make it null for a fixed $r$, since the component on the $z$ direction will be constant but the radial is $\theta$ dependent. What can be made, as @mcodesmart posted is to get a zero flux on a sphere. In this case, the radial field will be zero. For this we must have $$\frac{\mu_0m_0}{4\pi}\frac{3\cos\theta-\cos\theta}{r^3}+B_0\cos \theta=0\implies\\ r=\left(-\frac{\mu_0m_0}{2\pi B_0}\right)^{1/3}$$ which shows that the uniform field must be in the opposite sign of the dipole.

As the other answers already pointed out, there's no such spheric region. The field produced by the magnetic dipole will be given by $$\mathbf{B}_d(r,\theta)=\frac{\mu_0m_0}{4\pi}\frac{3\hat{\mathbf{r}}\cos\theta-\hat{\mathbf{z}}}{r^3}$$ So, adding both fields, we cannot make it null for a fixed $r$, since the component on the $z$ direction will be constant but the radial is $\theta$ dependent. What can be made, as @mcodesmart posted is to get a zero flux on a sphere. In this case, the radial field will be zero. For this we must have $$\frac{\mu_0m_0}{4\pi}\frac{3\cos\theta-\cos\theta}{r^3}+B_0\cos \theta=0\implies\\ r=\left(-\frac{\mu_0m_0}{2\pi B_0}\right)^{1/3}$$ which shows that the uniform field must be oriented in the opposite sense of the dipole.

As the other answers already pointed out, there's no such spheric region. The field produced by the magnetic dipole will be given by $$\mathbf{B}_d(r,\theta)=\frac{\mu_0m_0}{4\pi}\frac{3\hat{\mathbf{r}}\cos\theta-\hat{\mathbf{z}}}{r^3}$$ So, adding both fields, we cannot make it null for a fixed $r$, since the component on the $z$ direction will be constant but the radial is $\theta$ dependent. What can be made, as @mcodesmart posted is to get a zero flux on a sphere. In this case, there'll be only the radial field and the vertical component will be zero. For this we must have $$\frac{\mu_0m_0}{4\pi}\frac{1}{r^3}=B_0\implies\\ r=\left(\frac{\mu_0m_0}{4\pi B_0}\right)^{1/3}$$

As the other answers already pointed out, there's no such spheric region. The field produced by the magnetic dipole will be given by $$\mathbf{B}_d(r,\theta)=\frac{\mu_0m_0}{4\pi}\frac{3\hat{\mathbf{r}}\cos\theta-\hat{\mathbf{z}}}{r^3}$$ So, adding both fields, we cannot make it null for a fixed $r$, since the component on the $z$ direction will be constant but the radial is $\theta$ dependent. What can be made, as @mcodesmart posted is to get a zero flux on a sphere. In this case, the radial field will be zero. For this we must have $$\frac{\mu_0m_0}{4\pi}\frac{3\cos\theta-\cos\theta}{r^3}+B_0\cos \theta=0\implies\\ r=\left(-\frac{\mu_0m_0}{2\pi B_0}\right)^{1/3}$$ which shows that the uniform field must be in the opposite sign of the dipole.