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Q.

A long solenoid carrying a current produces a magnetic field B1 along its axis. If the current is four times and number of turns per cm is halved, the new value of magnetic field will be equal to $B_{2} = x B_{1}$ , then $x$ is

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answer is 2.

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Detailed Solution

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Magnetic field due to solenoid is given by

$B = μ_{0} n I B α n I$

$\frac{B_{2}}{B_{1}} = \frac{n_{2} I_{2}}{n_{1} I_{1}} = \frac{n 4 I}{2 n I} = 2$

$B_{2} = 2 B_{1}$

$x' = 2$

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A long solenoid carrying a current produces a magnetic field B1 along its axis. If the current is four times and number of turns per cm is halved, the new value of magnetic field will be equal to B2=xB1, then x is