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AP Physics 2
12.4 Electromagnetic Induction and Faraday’s Law
12.1 Magnetic Fields
AdvancedMCQMathematicalConceptual22.6k
A schematic side view of a horizontal cylindrical solenoid. A central longitudinal line represents the solenoid axis, along which horizontal arrows represent the uniform magnetic field vector B pointing to the right. An inclined planar sheet inside the solenoid spans the inner diameter 2R. A dashed vector labeled n-hat points normal to the sheet, making an angle theta with the magnetic field vector B. The solenoid radius R is indicated vertically. No other labels, lines, text, or axes appear.
Side view of a long solenoid containing an inclined planar surface.
A long solenoid of radius \(R\) has \(n\) turns per unit length and carries a constant direct current \(I\). A flat sheet is placed inside the solenoid such that its perimeter touches the inner walls of the solenoid, completely spanning the interior cross-section. The sheet is tilted so that its surface normal vector makes an angle \(\theta\) with the central longitudinal axis of the solenoid, where \(0 \le \theta < \frac{\pi}{2}\). The surface area of the tilted sheet is \(A = \dfrac{\pi R^2}{\cos\theta}\). Which of the following expressions represents the magnetic flux \(\Phi_B\) through the tilted sheet?

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