Question

A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given `"N"/12`µ₀aJ, then the value of N is ______.

पर्याय

• 5

• 6

• 7

• 4

Answer 1

A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given `"N"/12`µ₀aJ, then the value of N is 5.

Explanation:

B_R = B_T - B_C

R = Remaining portion

T = Total portion and

C = Cavity

B_R = `(mu_0"I"_"T")/(2"a"pi)-(mu_0"I"_"C")/(2(3"a"//2)pi)`      ...(i)

I_T = J(πa²)

I_C = J`((pi"a"^2)/4)`

Substituting the values in Eq. (i), we have

B_R = `mu_0/("a"pi)[(pi"a"^2"J")/2-(pi"a"^2"J")/12]`

= `(5mu_0"aJ")/12`

∴ N = 5