Revision: Class 12 >> Magnetic Effect of Current NEET (UG) Magnetic Effect of Current

Current passed through each of the two infinitely long parallel straight conductors kept at a distance of one meter apart in vacuum causes each conductor to experience a force of 2 × 10^-7 newton per meter length of the conductor.

A long solenoid is a coil whose length is much greater than its radius, producing a uniform magnetic field inside and nearly zero field outside.

The current sensitivity of a galvanometer is defined as the deflection produced in the galvanometer when a unit current flows through it.  
Mathematically, it can be given by:

I_S = `(NBA)/k`

Where k is the couple per unit twist.

Current sensitivity is defined as the deflection e per unit current.

\[\vec{E}=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}\hat{r}\]

\[\vec{B}=\frac{\mu_0IR^2}{2(x^2+R^2)^{3/2}}\hat{i}\]

Where:

• I = current
• R = radius of loop
• x = distance from centre along axis
• μ0 = permeability of free space

B = μ₀​nI

Where:

• μ_0​ = permeability of free space
• n = number of turns per unit length
• I = current

\[\vec{m}=I\vec{A}\]

For N turns:

\[\vec{m}=NI\vec{A}\]

\[B=\frac{\mu_0}{4\pi}\frac{2m}{x^3}\]

Magnetic Field on the Equatorial Line (for x ≫ R)

\[B=\frac{\mu_0}{4\pi}\frac{m}{x^3}\]

The toroid is a solenoid bent into the shape of a hollow doughnut.

According to Ampere's circuital law.

`phivecB.vec(dL) = mu_0I`

Here current 'I' flow through the ring as many times as there are the N no. of turns.

∴ `phivecB.vec(dL) = mu_0NI` ......(1)

Now, B and dL are in the same direction.

∴ `phivecB.vec(dL) = BphidL`

∴ `phivecB.vec(dL) = B.(2pir)` .....(2)

From (1) and (2),

`mu_0NI = B.(2pir)`

∴ B = `(mu_0NI)/(2pir)`