A circular coil connected to a battery of emf E produced a certain magnetic induction field at its centre. The coil is unwound, stretched to double its length rewound into a coil of 1 rd 3 of the original radius and connected to a battery of emf E ' to produce same field at the centre. Then E ' is

Step-by-step solution

The expression for the magnetic field at the centre of a circular coil of n turns. B = μ 0 i 2 r n If length of the wire is doubled, 2   2 π r n = 2 π r ' n ' 2   r   n = r 3 n ' n ' = 6 n For the same field at the centre, μ 0 i n 2 r = μ 0 i ' n ' 2 r ' μ 0 i n 2 r = μ 0 i   6   n 2   r 3 ⇒     i ' = i 18 Since volume will remain same. ∴       l × A = 2 l × A ' ⇒