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A current I(t) = Io cos(@t) flows through a long solenoid with n turns per meter and radius R, where Io is the current amplitude and wo is the angular frequency. Derive an expression for the magnitude of the induced electric field Ein (r, t) inside the solenoid as a function of the distance r from the solenoid's central axis and the time t. Your expression may include the variables Io, w, R, n, and the permeability of free space μ. Ein (r, t) = Incorrect Eout(r, t) = (¹0² Incorrect - cos (wt) R Derive an expression for the magnitude of the induced electric field Eout(r, t) outside the solenoid as a function of r and t. Your expression may include the variables Io, w, R, n, and μo. . n. cos (1o-n.cos(wt)) R

A current I(t) = Io cos(@t) flows through a long solenoid with n turns per meter and radius R, where Io is the current amplitude and wo is the angular frequency. Derive an expression for the magnitude of the induced electric field Ein (r, t) inside the solenoid as a function of the distance r from the solenoid's central axis and the time t. Your expression may include the variables Io, w, R, n, and the permeability of free space μ. Ein (r, t) = Incorrect Eout(r, t) = (¹0² Incorrect - cos (wt) R Derive an expression for the magnitude of the induced electric field Eout(r, t) outside the solenoid as a function of r and t. Your expression may include the variables Io, w, R, n, and μo. . n. cos (1o-n.cos(wt)) R

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I don't know how else I could structure the equation for this problem could you please help me figure out what I am missing here?

A current I(t) = Io cos(@t) flows through a long solenoid with n turns per meter and radius R, where Io is the current amplitude and wo is the angular frequency. Derive an expression for the magnitude of the induced electric field Ein(r, t) inside the solenoid as a function of the distance r from the solenoid's central axis and the time t. Your expression may include the variables Io, w, R, n, and the permeability of free space μo- Ein (r, t) = Incorrect Eout(r, t) = (10 Derive an expression for the magnitude of the induced electric field Eout(r, t) outside the solenoid as a function of r and t. Your expression may include the variables Io, w, R, n, and μ. Incorrect . n. - cos (wt) R (1o-n.cos(wt)) R
Transcribed Image Text:A current I(t) = Io cos(@t) flows through a long solenoid with n turns per meter and radius R, where Io is the current amplitude and wo is the angular frequency. Derive an expression for the magnitude of the induced electric field Ein(r, t) inside the solenoid as a function of the distance r from the solenoid's central axis and the time t. Your expression may include the variables Io, w, R, n, and the permeability of free space μo- Ein (r, t) = Incorrect Eout(r, t) = (10 Derive an expression for the magnitude of the induced electric field Eout(r, t) outside the solenoid as a function of r and t. Your expression may include the variables Io, w, R, n, and μ. Incorrect . n. - cos (wt) R (1o-n.cos(wt)) R
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I tried this equation but it still isn't correct I have no idea what to do since the equation for the eletric field outside the solonoid is not zero

### Transcription **Problem Statement:** A current \( I(t) = I_0 \cos(\omega t) \) flows through a long solenoid with \( n \) turns per meter and radius \( R \), where \( I_0 \) is the current amplitude and \( \omega \) is the angular frequency. **Task 1:** Derive an expression for the magnitude of the induced electric field \( E_{\text{in}}(r, t) \) inside the solenoid as a function of the distance \( r \) from the solenoid's central axis and the time \( t \). Your expression may include the variables \( I_0, \omega, R, n \), and the permeability of free space \( \mu_0 \). **Incorrect Expression:** \[ E_{\text{in}}(r, t) = \frac{l \cdot n^2 \cdot I_0 \cdot \pi \cdot r^2 \omega \sin(\omega t)}{R} \] **Task 2:** Derive an expression for the magnitude of the induced electric field \( E_{\text{out}}(r, t) \) outside the solenoid as a function of \( r \) and \( t \). Your expression may include the variables \( I_0, \omega, R, n \), and \( \mu_0 \). **Incorrect Expression:** \[ E_{\text{out}}(r, t) = \frac{l \cdot n^2 \cdot I_0 \cdot \pi \cdot r^2 \omega \sin(\omega t)}{R} \]
Transcribed Image Text:### Transcription **Problem Statement:** A current \( I(t) = I_0 \cos(\omega t) \) flows through a long solenoid with \( n \) turns per meter and radius \( R \), where \( I_0 \) is the current amplitude and \( \omega \) is the angular frequency. **Task 1:** Derive an expression for the magnitude of the induced electric field \( E_{\text{in}}(r, t) \) inside the solenoid as a function of the distance \( r \) from the solenoid's central axis and the time \( t \). Your expression may include the variables \( I_0, \omega, R, n \), and the permeability of free space \( \mu_0 \). **Incorrect Expression:** \[ E_{\text{in}}(r, t) = \frac{l \cdot n^2 \cdot I_0 \cdot \pi \cdot r^2 \omega \sin(\omega t)}{R} \] **Task 2:** Derive an expression for the magnitude of the induced electric field \( E_{\text{out}}(r, t) \) outside the solenoid as a function of \( r \) and \( t \). Your expression may include the variables \( I_0, \omega, R, n \), and \( \mu_0 \). **Incorrect Expression:** \[ E_{\text{out}}(r, t) = \frac{l \cdot n^2 \cdot I_0 \cdot \pi \cdot r^2 \omega \sin(\omega t)}{R} \]
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