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## Homework Statement

A constant direct current of uniform density ##\vec{j}## is flowing in an infinitely long cylindrical conductor. The conductor contains an infinitely long cylindrical cavity whose axis is parallel to that of the conductor and is at a distance ##\vec{\ell}## from it. What will be the magnetic induction ##\vec{B}## at a point inside the cavity at a distance ##\vec{r}## from the centre of cavity?

A)##\frac{\mu_0(\vec{j} \times \vec{r})}{2}##

B)##\frac{\mu_0(\vec{j} \times \vec{l})}{2}##

C)##\frac{\mu_0(\vec{j} \times \vec{r})+\mu_0(\vec{j} \times \vec{\ell})}{2}##

D)##\frac{\mu_0(\vec{j} \times \vec{\ell})+\mu_0(\vec{j} \times \vec{r})}{2}##

## Homework Equations

## The Attempt at a Solution

I have done similar questions in electrostatics so I think the same procedure can be applied. The procedure in electrostatics involves considering the cavity as oppositely charged cylinder and find the resultant field (I hope I explained it correctly). So here in this case, I can consider the cylindrical cavity with a uniform current density of ##\vec{-j}##. I can easily calculate the magnetic field inside a cylinder which comes out to ##\frac{\mu_0Iz}{2\pi R^2}## where z is the distance from axis but the problem is how would I write it in the form of cross products?

Any help is appreciated. Thanks!