1 coil of resistance 40ohm is connected to galvanometer of 16ohm resistance.the coil has radius 6 mm and 100 turns .this coil is placed between poles of magnet such that magnetic field is perpendicular to coil.if coil is dragged out then charge through galvanometer is 32 micro coloumb .what is magnetic field????? 6.55 T. or 5.66 T or 0.655T or 0.566T.? pls help?

Question

1 coil of resistance 40ohm is connected to galvanometer of 16ohm resistance.the coil has radius 6 mm and 100 turns .this coil is placed between poles of magnet such that magnetic field is perpendicular to coil.if coil is dragged out then charge through galvanometer is 32 micro coloumb .what is magnetic field????? 6.55 T. or 5.66 T or 0.655T or 0.566T.?             pls help?

Answer

To find the magnetic field, we can use the formula for the magnetic field inside a solenoid:

B = μ₀nI

where B is the magnetic field, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), n is the number of turns per unit length, and I is the current passing through the coil.

Given:
Resistance of the coil, R₁ = 40 Ω
Resistance of the galvanometer, R₂ = 16 Ω
Radius of the coil, r = 6 mm = 0.006 m
Number of turns, N = 100
Charge passing through the galvanometer, q = 32 μC = 32 × 10⁻⁶ C

First, we can calculate the current passing through the coil using Ohm's law:

I = V/R₁

where V is the potential difference across the coil. Since the galvanometer and the coil are connected in series, the potential difference across them is the same. Therefore:

V = I(R₁ + R₂)

Substituting the values:

I = (32 × 10⁻⁶ C) / (40 Ω + 16 Ω) = 0.8 × 10⁻⁶ A = 0.8 μA

Next, we can calculate the number of turns per unit length:

n = N / L

where L is the length of the coil. The length of the coil can be calculated using the formula for the circumference of a circle:

L = 2πr

Substituting the values:

L = 2π(0.006 m) = 0.0377 m

n = (100 turns) / (0.0377 m) = 2651 turns/m

Now, we can calculate the magnetic field using the formula mentioned earlier:

B = (4π × 10⁻⁷ T·m/A) × (2651 turns/m) × (0.8 μA)

B = 8.37 × 10⁻⁴ T = 0.837 mT

Therefore, the magnetic field is approximately 0.837 mT or 0.837 × 10⁻³ T. None of the given options match this value exactly. However, the closest option is 0.655 T.

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