# is it possible to shape electromagnetic field?

Is it possible to produce a magnetic field of specific shape? For example a magnetic field that will be confined in a cylindrical shape of specific dimensions.

• It's a yes...but. While you haven't sufficiently specified what kind of field you want, I have a hunch that what you are asking for will be impossible. One can constrain a field to a cylindrical region, but it won't be a cylindrical homogeneous field. That is impossible. – CuriousOne Apr 22 '16 at 20:59

## 2 Answers

Maxwell's equations constrain what fields you can produce. Write down the field you are thinking of and check it for yourself! Suppose you want to create the field $\vec{B}(t,x,y,z)$. It must satisfy Gauss's law ($\nabla\cdot\vec{B}=0$ for every point in space and every time). This is a big constraint on the types of fields you can create. If the $\vec{B}$ you have in mind does satisfy Gauss's law then the other Maxwell's equations tell you what kind of $\vec{E}$, $\vec{J}$ and $\rho$ you need to produce the desired $\vec{B}$. If you want $\vec{E}=0$ then you have more constraints, for instance $\vec{B}$ cannot be a function of time. Then you just need a steady current $\vec{J}=\nabla\times\vec{B}$ and you can get your desired $\vec{B}$ field.

Using phased array antennas you can direct electromagnetic radiation into preferred directions, while suppressing in other directions. These work by arranging the relative phases of signals feeding the antenna array so that the effective radiation pattern of the array is reinforced (via constructive interference) in a particular direction and suppressed in other directions (via destructive interference.

• so, a metallic part will be attracted only when it is inside that cylinder and not if it is outside? – ergon Apr 23 '16 at 11:13
• Each antenna of the array creates an em field, by properly choosing the currents in each antenna (the size of the current and its phase) the total em field can be made to made bigger or smaller. – jim Apr 23 '16 at 11:27