Question

A current $I$ flows along a lengthy thin-walled tube of radius $R$ with longitudinal slit of width $h.$ Find the magnetic field inside the tube under the condition $h<

• A. Zero
• B. $\frac{{\mu }_{0}hI}{2{\pi }^{2}Rr}$
• C. $\frac{{\mu }_{0}hI}{4{\pi }^{2}R}$
• D. $\frac{{\mu }_{0}hI}{4{\pi }^{2}Rr}$

Answer 1

The correct option is D $\frac{{\mu }_{0}hI}{4{\pi }^{2}Rr}$

The correct option is D.

Given,

A current $I$ flows along a lengthy thin-walled tube of radius $R$

$width=h$

Net current is flowing in an upward direction. At point P, the magnetic field will be zero if silt is not present. now the field is only due to silt wire.

$\Rightarrow B=\frac{{\mu }_0}{2\pi R}\left(I\text{'}\right).....1$

Where $I^{\prime }$ is the current of the slit.

Then,

$I\text{'}=\frac{Ih}{2\pi R}$

Put this value in equation 1 then we get,

$B=\frac{{\mu }_0}{2\pi R}\times \frac{Ih}{2\pi R}$

Thus, the magnetic field inside the tube under the condition is:

$B=\frac{{\mu }_{0}hI}{4{\pi }^{2}Rr}$