(Solved): Show me the steps to solve 8. A current \( I \) flows through a plane wire coil of radius \( a \) wi ...

Show me the steps to solve 8. A current \( I \) flows through a plane wire coil of radius \( a \) with \( N \) turns. Find an expression for the magnetic flux density at a distance \( x \) along the principal axis of the coil from the centre. A second identical coil is placed parallel to and coaxial with the first, and separated by a distance \( a \). Identical currents \( I \) flow through the coils in the same direction. What is the magnetic flux density \( B \) on the axis midway between the pair of coils and at the centre of each coil? Sketch the total magnetic flux density and the contribution from each coil as a function of position on the axis between the coils. Describe briefly the properties of this coil arrangement. A stream of electrons is accelerated by a potential \( V \) and introduced into the region between the coils, perpendicular to the principal axis of the coils and close to the mid-point. An experimenter wants to deflect the electron stream so that it emerges from the region between the coils travelling parallel to but in the opposite direction to the input stream and separated by 2 cm . What is the value of the magnetic flux density between the coils required to achieve this, when the accelerating potential \( V=10 \mathrm{kV} \) ? [You may neglect the effects of any \( B \) field external to the space between the two coils, and assume that the radius of the coils is \( \gg 2 \mathrm{~cm} \).]