Exams › JEE Advanced › Physics

In a string-theory model, the extra hidden dimension y is compactified on the surface of a thin cylinder of radius b. An electromagnetic wave on the surface takes the form E(x, y) = A*sin(kₓ * x)*cos(k_y * y), where y is the coordinate around the cylinder. Find the allowed values of k_y (m = 1, 2, 3,...).

1. k_y = m/b
2. k_y = m/(2b)
3. k_y = m/(pi*b)
4. k_y = 2m/(pi*b)

Correct answer: k_y = m/b

Solution

The coordinate y is periodic with period 2*pi*b (circumference of the cylinder). For the wave to be single-valued, k_y*(2*pi*b) must be a multiple of 2*pi, giving k_y = m/b.

Related JEE Advanced Physics questions

• Rain is falling at an angle α with respect to the vertical at a velocity of 10 m/s. A girl runs in the opposite direction to the rain at a speed of 8 m/s and observes that the rain appears to make an angle β with the vertical. What is the relationship between α and β?
• A vector A is turned by a very small angle Δθ radians (where Δθ is much less than 1) to form a new vector B. What is the magnitude of the difference |B − A|?
• A swimmer moves through water at a speed of v relative to the water. To cross a river of width d, which flows at a speed u (where u < v), the downstream displacement caused by the river's flow is x. Which of the following is accurate?
• A particle is launched from a point with an initial speed u at an angle θ above the horizontal. At a specific point during its motion, its velocity becomes perpendicular to its original direction. What is the time taken to reach this point?
• Two objects, each with a mass of M, are positioned at a fixed distance of 2L apart. A smaller particle of mass m is launched from the midpoint of the line connecting their centers, moving in a direction perpendicular to this line. Given the gravitational constant G, which of the following statements is accurate?
• A central force is given as F(r) = −k / rⁿ, where k is a constant. What condition must n satisfy for a circular orbit to remain stable?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →