Question

A winding wire is used to prepare a solenoid that can bear a maximum current of 10A. If the length of a solenoid is 80 cm and its cross-sectional radius is 3 cm, the required length of winding wire is ____________.

(magnetic field B = 0.2 T, µ₀ = 4 x 10^-7 SI units)

Options

• 2.4 x 10³ m

• 1.8 x 10³ m

• 2.1 x 10³ m

• 1.5 x 10³ m

Answer 1

A winding wire is used to prepare a solenoid that can bear a maximum current of 10A. If the length of a solenoid is 80 cm and its cross-sectional radius is 3 cm, the required length of winding wire is 2.4 x 10³ m.

Explanation:

`"T" = 10 "A", varphi = 80  "cm" - 0.8  "m",`

r = 3 cm = 3 x 10^-2 m, N = number or turns

`"B" = (mu_0 "NI")/varphi`

`therefore "N" = ("B"  varphi)/(mu_0  "I")`

Length of the wire L `= 2pi"rN" = (2pi"rB" varphi)/(mu_0 "I")`

substituting the values and calculating we get L = 2.4 x 10³ m