A galvanometer of resistance 100Ω$100\Omega$ gives full scale deflection for a current of 1 ~mA$1 \mathrm{~mA}$. It is converted into an ammeter of range 0--10 ~A$0\text{--}10 \mathrm{~A}$. The shunt required is:

Related Formula

Core Logic

First, calculate the current i$i$ using the magnetic field formula for a circular loop:

Substitute the given values: R = 5 × 10⁻² ~m$R = 5 \times 10^{-2} \mathrm{~m}$ B₀ = 3.14 × 10⁻³ ~T$B_0 = 3.14 \times 10^{-3} \mathrm{~T}$ N = 100$N = 100$

Using π ≈ 3.14$\pi \approx 3.14$, we get:

Step 1: Calculate Magnetic Moment

Now, compute the magnetic moment M$M$:

M = N i π R²$M = N i \pi R^2$

Pattern Recognition

Recognize that π ≈ 3.14$\pi \approx 3.14$ cancels out nicely when substituted directly against the given magnetic field value.

Chapter Mix

Class 12 Physics: Moving Charges and Magnetism

Related Formula

Core Logic

For a long straight solid wire carrying a steady current that is uniformly distributed across its cross-section:

• Inside the wire (r < a$r < a$), the magnetic field is directly proportional to the distance from the axis (B ∝ r$B \propto r$). This represents a straight line passing through the origin.
• Outside the wire (r > a$r > a$), the magnetic field is inversely proportional to the distance from the axis (B ∝ (1)/(r)$B \propto \frac{1}{r}$). This represents a rectangular hyperbola.

Step 1: Graph Identification

The correct graph must show a linear increase starting from the origin up to r=a$r=a$, followed by a smooth 1/r$1/r$ hyperbolic curve decaying towards zero for r>a$r>a$. The plot matching this criteria is option 1.

Pattern Recognition

Solid cylinder uniform current: Inside B ∝ r$B \propto r$ (linear), outside B ∝ 1/r$B \propto 1/r$ (curve). Hollow cylinder: Inside B = 0$B = 0$, outside B ∝ 1/r$B \propto 1/r$.

Chapter Mix

Class 12 Physics: Moving Charges and Magnetism