A device called a toroid (figure) is often used to create an almost uniform magetic fiedl in some enclosed area. The device consists of a conducting wire wraped around a ring (a torus) made of a non conducting material. For a toroid having `N` closely spaced turns of wire, calculate the magnetic field in the region occupied by the torus, a distasnce `r` from the centre.
A device called a toroid (figure) is often used to create an almost uniform magetic fiedl in some enclosed area. The device consists of a conducting wire wraped around a ring (a torus) made of a non conducting material. For a toroid having `N` closely spaced turns of wire, calculate the magnetic field in the region occupied by the torus, a distasnce `r` from the centre.
Text Solution
AI Generated Solution
To calculate the magnetic field inside a toroid at a distance \( r \) from the center, we can follow these steps:
### Step 1: Understand the Configuration
A toroid is a ring-shaped object made by wrapping a conducting wire around a non-conducting material. It has \( N \) closely spaced turns of wire and carries a current \( I \).
### Step 2: Apply Ampere's Law
According to Ampere's Law, the line integral of the magnetic field \( B \) around a closed loop is equal to the permeability of free space \( \mu_0 \) times the total current \( I_{\text{enc}} \) enclosed by the loop:
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