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`        The current in an ideal, long solenoid is varied at a uniform rate of 0.01 A/s. The solenoid has 2000 turns/m and its radius is 6.0 cm. (a) Consider a circle of with the axis of the solenoid. Write the change in the magnetic flux through this circle in 2.0 seconds. (b) Find the electric field induced at a point on the circumference of the circle. (c) Find the electric field induced at a point outside the solenoid at a distance 8.0 cm from its axis.`
5 years ago 396 Points
```							Sol. di/dt = 0.01 A/s
For 2s di/dt = 0.02 A/s
n = 2000 turn/m, R = 6.0 cm = 0.06 m
r = 1 cm = 0.01 m
a) ϕ = BA
⇒ dϕ/dt = μ base 0 nA di/dt
= 4π × 10^–7 × 2 × 10^3 × π × 1 × 10^–4 × 2 × 10^–2  [A = π × 1 × 10^–4]
= 16π^2 × 10^–10 ω
= 157.91 ×10^–10 ω
= 1.6 × 10–8 ω
or, dϕ/dt for 1 s=0.785 ω.
(b) ∫▒〖E.〗dl = dϕ/dt
⇒ Eϕdl = dϕ/dt ⇒ E = 0.785x10^-8/2π x 10^-2 = 1.2 x 10^-7 V/m
(c) dϕ/dt = μ base 0 n di/dt A = 4π x 10^-7 x 2000 x 0.01 x π x (0.06)^2
Eϕdl = dϕ/dt
⇒ E dϕ/dt/2πr = 4π x 10-7 x 2000 x 0.01 x π x (0.06)^2 = 5.64 x 10^-7 V/m

```
5 years ago
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