Introduction:
A moving coil instrument is a type of electromagnetic instrument used for measuring current or voltage in electrical circuits. It consists of a coil that is free to rotate in a magnetic field. When current flows through the coil, a torque is generated, causing the coil to deflect. The deflection can be measured and used to determine the current or voltage being measured.

Given data:
Number of turns (N) = 100
Width of coil (W) = 20 mm
Depth of coil (D) = 30 mm
Flux density in the gap (B) = 0.1 Wb/m^2
Current (I) = 10 mA

Calculating the area of the coil:
The area of the coil can be calculated using the formula:

Area (A) = Width (W) x Depth (D)

Substituting the given values:

A = 20 mm x 30 mm = 600 mm^2

Calculating the magnetic flux:
The magnetic flux through the coil can be calculated using the formula:

Flux (Φ) = Magnetic field (B) x Area (A)

Substituting the given values:

Φ = 0.1 Wb/m^2 x 600 mm^2 = 0.06 Wb

Calculating the torque:
The torque exerted on the coil can be calculated using the formula:

Torque (τ) = Number of turns (N) x Flux (Φ) x Current (I)

Substituting the given values:

τ = 100 x 0.06 Wb x 10 mA = 60 x 10^-3 Nm

Therefore, the deflection torque when carrying a current of 10 mA is 60 x 10^-3 Nm.

Explanation:
- A moving coil instrument is a type of electromagnetic instrument used for measuring current or voltage in electrical circuits.
- It consists of a coil that is free to rotate in a magnetic field.
- When current flows through the coil, a torque is generated, causing the coil to deflect.
- The deflection can be measured and used to determine the current or voltage being measured.
- In this case, we are given the number of turns, width of the coil, depth of the coil, flux density in the gap, and current.
- We first calculate the area of the coil by multiplying the width and depth.
- Next, we calculate the magnetic flux through the coil by multiplying the flux density and area.
- Finally, we calculate the torque exerted on the coil by multiplying the number of turns, flux, and current.
- The calculated torque represents the deflection torque when carrying a current of 10 mA.
- This torque can be used to determine the deflection angle of the coil, which can then be used to measure the current or voltage being measured.