Question

A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coil is perpendicular to the direction of magnetic field. The magnetic field is reduced uniformly to zero in 20 ms and again increased uniformly to 30 mT in 40 ms. If the emfs induced in the two time intervals are e₁ and e₂ respectively, then the value of e₁/e₂ is ______.

पर्याय

• `1/2`

• 1

• 2

• 4

Answer 1

A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coil is perpendicular to the direction of magnetic field. The magnetic field is reduced uniformly to zero in 20 ms and again increased uniformly to 30 mT in 40 ms. If the emfs induced in the two time intervals are e₁ and e₂ respectively, then the value of e₁/e₂ is 2.

Explanation:

Given: Diameter of the coil (d) = 0.015 m = 15 mm

Number of turns (N) = 300

Magnetic field (B) = 30 mT

Case 1:

Initial magnetic field (B_i) = 30 mT

Final magnetic field for first interval (B_f) = 0

Time for first interval (t) = 20 ms

e₁ = ?

Case 2:

Initial magnetic field (B_i) = 0

Final magnetic field for first interval (B_f) = 30 mT

Time for second interval (t) = 40 ms

e₂ = ?

`e_1/e_2` = ?

The induced emf is:

E = `-N ((d phi)/dt)`

= `-Nd/dt B xx A`

= `-N(dB)/dt`

= `-NA[(B_f - B_i)/t]`

For case 1:

e₁ = `-NA[(0 - 30 xx 10^-3)/(20 xx 10^-3)]`

|e₁| = `3/2`

For case 2:

e₂ = `-NA[(30 xx 10^-3 - 0)/(40 xx 10^-3)]`

|e₂| = `3/4`

∴ `e_1/e_2 = (3/2)/(3/4)`

= 2