A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field
Q. A simple pendulum made of mass $10\,\text{g}$ and a metallic wire of length $10\,\text{cm}$ is suspended vertically in a uniform magnetic field of $2\,\text{T}$. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^\circ$ with vertical, then maximum induced EMF between the point of suspension and point of oscillation is _____ mV. (Take $g = 10\,\text{m/s}^2$)
Correct Answer: 100

Explanation

When a conductor moves in a magnetic field, the induced EMF is given by

$$ \varepsilon = B \, l \, v $$

Maximum induced EMF occurs when the velocity of the pendulum is maximum, i.e., at the mean position.

Using energy conservation, the maximum speed of the pendulum bob is obtained from

$$ \frac{1}{2}mv^2 = mgL(1-\cos\theta) $$

Here,

$$ L = 0.1\,\text{m}, \quad \theta = 60^\circ $$

$$ 1 - \cos 60^\circ = 1 - \frac{1}{2} = \frac{1}{2} $$

So,

$$ v = \sqrt{2gL \cdot \frac{1}{2}} = \sqrt{gL} $$

$$ v = \sqrt{10 \times 0.1} = 1\,\text{m/s} $$

Now, substituting values in the EMF formula,

$$ \varepsilon_{\max} = B \, l \, v $$

$$ = 2 \times 0.1 \times 1 = 0.2\,\text{V} $$

Since EMF is induced across half the oscillation length effectively contributing,

$$ \varepsilon_{\max} = 0.1\,\text{V} = 100\,\text{mV} $$

Hence, the maximum induced EMF is

$$ \boxed{100} $$

Related JEE Main Questions

Updated for JEE Main 2026: This PYQ is important for JEE Mains, JEE Advanced and other competitive exams. Practice more questions from this chapter.

Scroll to Top