Question

Questions
Two circular coils made of same material of radii 40 cm and 50 cm having number of turnns 50 and 100 are connected in
parallel. The ratio of the magnetic field of induction at their centres is​

Answer 1

Explanation:

Ratio = ratio of number of turns × area

$\frac{40}{50 } \times \frac{50}{100}$

=0.4

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Answer 2

Answer:

The ratio of the magnetic field of induction at their centres is​ $25:16$

Explanation:

Given,

The radii of the circular coil 1, r₁ = $40 cm$

The radii of the circular coil 2, r₂ = $50 cm$

The number of turns of circular coil 1 = $50$

The number of turns of circular coil 2 = $100$

As given,

The coils are connected in parallel.

The magnetic field's ratio of induction at their centres =?

As we know,

• The magnetic field of induction at their centres is given by the equation:
• B = $\frac{\mu nI}{2r}$  

Here,

• B = The magnetic field
• μ = The permeability constant
• n = The number of turns
• r = The coil's radius

After removing the constant terms, we get:

• B = $\frac{nI}{r}$    -------equation (1)

Now, as given, the coils are connected in parallel current will vary.

• $I = \frac{V}{R}$

Here,

• V = Potential difference
• R = Resistance

The potential difference is constant in parallel

Therefore,

• $I\alpha \frac{1}{R}$   ------equation (2)

Also,

• $R = \frac{\rho (n\pi r)}{A}$

Here,

• ρ = Resistivity
• n = The number of turns
• r = Radius
• A = Area

As the coils are made up of the same material, the resistivity and area will be constant.

Thus,

• R $\alpha nr$

After putting this in equation (2), we get:

• $I \alpha \frac{1}{nr}$

After putting this in equation (1), we get:

• B = $\frac{n}{r (nr)}$
• B = $\frac{1}{r^{2} }$

Now, the ratio of the magnetic field of the coils of induction at their centres is:

• $\frac{B_{1} }{B_{2} } = \frac{r_{2}^{2} }{r_{1}^{2} }$
• $\frac{B_{1} }{B_{2} } = \frac{(50)^{2} }{(40)^{2} }$
• $\frac{B_{1} }{B_{2} } = \frac{25 }{16 }$

Hence, the ratio of the magnetic field of the coils of induction at their centres is $25:16$.