Question

In a moving coil galvanometer, the magnetic field is made radial so that the:

• A. Resistance decreases
• B. Current sensitivity decreases
• C. Deflection becomes directly proportional to current
• D. Coil does not rotate

Hint:

A radial magnetic field ensures that $\sin\theta = 1$ at all times. This eliminates angular distortion from the torque equation, ensuring a linear scale where deflection changes directly with current ($\alpha \propto I$).

Answer 1

The Correct Option is C

Concept: A moving coil galvanometer measures small electric currents using a current-carrying coil suspended in a uniform magnetic field. The deflecting torque ($\tau_d$) experienced by a coil with $N$ turns, area $A$, carrying current $I$ in a magnetic field $B$ is: \[ \tau_d = NIAB \sin\theta \] Where $\theta$ is the angle between the normal to the plane of the coil and the magnetic field lines.

Step 1: Understand the purpose and geometry of a radial magnetic field.
By using cylindrically concave permanent magnet poles alongside a soft iron core at the center, the magnetic field lines are bent radially. This ensures that as the coil rotates, its plane remains parallel to the magnetic field lines at all positions. Consequently, the angle between the normal to the coil's area and the field lines is always kept at exactly $\theta = 90^\circ$. Since $\sin(90^\circ) = 1$, the deflecting torque formula simplifies to its maximum value: \[ \tau_d = NIAB \]

Step 2: Link torque equilibrium to scale linearity.
The rotation is resisted by a suspension spring that creates a restoring torque ($\tau_r = k\alpha$), where $k$ is the torsional spring constant and $\alpha$ is the angular deflection. At equilibrium: \[ \tau_r = \tau_d \quad \implies \quad k\alpha = NIAB \] Solving for the angular deflection ($\alpha$): \[ \alpha = \left(\frac{NAB}{k}\right) I \quad \implies \quad \alpha \propto I \] Because the magnetic field is radial, the non-linear $\sin\theta$ term is eliminated. This makes the scale perfectly linear, meaning the angular Deflection is directly proportional to the current flowing through it.