JEE Advanced2012PhysicsElectrostaticsActual
An infinitely long solid cylinder of radius R has a uniform volume charge density . It has a spherical cavity of radius R / 2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P , which is at a distance 2 R from the axis of the cylinder, is given by the expression 23 R 16 K ₀ . The value of k is
Correct answer
0
Step-by-step solution
The magnitude of the electric field at the point P which is at a distance 2 R from the axis of the cylinder array l E = E _ total - E _ cavity = 2 ₀(2 R) - 1 4 ₀ Q (2 R)² Q _ sphere = 4 3 ( R 2 )³ = R³ 6 array l _ cylinder = R² E= R² 4 ₀ R - 1 4 ₀ R³ / 6 4 R² = 23 R 96 ₀ = 23 R 16 6 ₀ k=6 array array