Question

A moving coil galvanometer has 1000 turns and each turn has an area 2.0 cm². The magnetic field produced by the magnet is 2 x 10^-2 tesla. The deflection in the coil is 30° when a current of 10 mA is passed through it. Find the torsional couple of the suspension wire. ​

Answer 1

> torsional couple of the suspension wire

is 7.63x10^-5

step by step explanation:-

Correct Question:

$\:$

A moving coil galvanometer has 1000 turns and each turn has an area 2.0 cm². The magnetic field produced by the magnet is 2 x 10^-2 tesla. The deflection in the coil is 30° when a current of 10 mA is passed through it. Find the torsional couple of the suspension wire

Given:

No. of turn => 1000

Area of each turn=> 2.0cm²

magnetic field =>2 x 10^-2

Angle due to deflection => 30°

Current=> 10mA

Formula:

I => (K/nAB)*θ

Approach:

1. we have to convert area into m²

2. we have to convert angle into radian

3. finally, we put values in formula and find it's value

Let's begin :-

1. converting area :-

=> 2 x 10^-4m²

2. converting to radian :-

we know that,

π radian = 180°

so,

1° = π/180 radian

30°= 30π/180 radian

or,

Hence, 30°=π/6 radian

now,

Main solution :-

putting the required value :-

I => (K/nAB)*θ

so,

K= InAB/θ

=>(10x10^-3A x 1000 x 2.0x10^-4 x 2 x 10^-2 )/(π/6 )

=>(10x10^-3x10^3x2x10^-4x2x10^-2)/(π/6)

=>(10^-3x2x2x10^-2)/(π/6)

=>(10^-5x4)/(π/6)

=>(24x10^-5)/π

=>(24x7x10^-5)/22

=>7.63x10^-5

Hence, torsional couple of the suspension wire

is 7.63x10^-5

I hope it's helpful!

I tried my best

Answer 2

$\huge\fbox\red{Question:}$

A moving coil galvanometer has 1000 turns and each turn has an area 2.0 cm². The magnetic field produced by the magnet is 2 x 10^-2 tesla. The deflection in the coil is 30° when a current of 10 mA is passed through it. Find the torsional couple of the suspension wire

$\fbox\pink{Given:}$

No. of turn ⇉ 1000

Area of each turn ⇉2.0cm²

magnetic field ⇉2 x 10^-2

Angle due to deflection ⇉ 30°

Current ⇉ 10mA

$\fbox\purple{Formula:}$

I ⇉ (K/nAB)*θ

$\fbox\blue{Approach:-}$

1. we have to convert area into m²

2. we have to convert angle into radian

3. finally, we put values in formula and find it's value

$\fbox\green{Let's begin :-}$

1. converting area :-

⇉ 2 x 10^-4m²

2. converting to radian :-

we know that,

π radian = 180°

so,

1° = π/180 radian

30°= 30π/180 radian

or,

Hence, 30°=π/6 radian

now,

$\fbox\orange{Main Solution :-}$

putting the required value :-

I ⇉ (K/nAB)*θ

so,

K= InAB/θ

⇉(10x10^-3A x 1000 x 2.0x10^-4 x 2 x ⠀10^-2 )/(π/6 )

⇉(10x10^-3x10^3x2x10^-4x2x10^-2)/(π/6)

⇉(10^-3x2x2x10^-2)/(π/6)

⇉(10^-5x4)/(π/6)

⇉(24x10^-5)/π

⇉(24x7x10^-5)/22

⇉7.63x10^-5

✶ Hence, torsional couple of the ⠀ ⠀suspension wire is 7.63x10^-5

⠀⠀⠀

⠀⠀⠀⠀✦ 7.63×10^–5