If a current of 2A give rise a magnetic flux of `5xx10^(-5)` weber/turn through a coil having 100 turns , then the magnetic energy stored in the medium surrounding by the coil is :-

Options

A. 5 joule
B. `5xx10^(-7)` joule
C. `5xx10^(-3)` joule
D. 0.5 joule

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the given values
- Current (I) = 2 A
- Magnetic flux per turn (Φ) = \(5 \times 10^{-5}\) Wb/turn
- Number of turns (N) = 100 turns

### Step 2: Calculate the total magnetic flux (Φ_total)
The total magnetic flux linked with the coil can be calculated using the formula:
\[ \Phi_{\text{total}} = N \times \Phi \]
Substituting the values:
\[ \Phi_{\text{total}} = 100 \times (5 \times 10^{-5}) = 5 \times 10^{-3} \text{ Wb} \]

### Step 3: Calculate the inductance (L)
The inductance (L) of the coil can be calculated using the formula:
\[ L = \frac{\Phi_{\text{total}}}{I} \]
Substituting the values:
\[ L = \frac{5 \times 10^{-3}}{2} = 2.5 \times 10^{-3} \text{ H} = 25 \times 10^{-4} \text{ H} \]

### Step 4: Calculate the magnetic energy (U) stored in the coil
The magnetic energy stored in the inductor can be calculated using the formula:
\[ U = \frac{1}{2} L I^2 \]
Substituting the values:
\[ U = \frac{1}{2} \times (25 \times 10^{-4}) \times (2^2) \]
Calculating further:
\[ U = \frac{1}{2} \times (25 \times 10^{-4}) \times 4 = 50 \times 10^{-4} \text{ J} = 5 \times 10^{-3} \text{ J} \]

### Final Answer:
The magnetic energy stored in the medium surrounding the coil is \(5 \times 10^{-3}\) Joules.

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