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A circular coil of 8 turns and a diameter of 30.0 cm is oriented in a vertical plane with its axisperpendicular to the horizontal component of the Earth's magneticfield. A horizontal compass placed at the center of the coil is made to deflect 45.0° from magnetic north by a current of 0.510 A in the coil.

a) What is the horizontal component of the Earth's magnetic field?
b) The current in the coil is switched off. A "dip needle" is amagnetic compass mounted so that it can rotate in a verticalnorth-south plane. At this location, a dip needle makes an angle of18.0° from the vertical. What is thetotal magnitude of the Earth's magnetic field at this location?

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