A length of conducting wire is bent into a circular coil of 7 turns. The diameter of the circle is 30.0 cm, and the axis of the coil is perpendicular to the horizontal component of the Earth's magnetic field. A horizontally-oriented compass is placed along the axis of the coil, directly in the center, and when a current of 0.540 A flows in the coil, the compass needle is deflected by 45° from magnetic north. Required:
a. What is the horizontal component of theEarth'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 of11.0° from the vertical. What isthe total magnitude of the Earth's magnetic field at thislocation?

a.  5.09 × 10⁻⁷ T b. 2.67 × 10⁻⁶ T

Explanation:

a. What is the horizontal component of the Earth's magnetic field?

The magnetic field due to the circular coil, B = μ₀Ni/L where μ₀ = 4π × 10⁻⁷ H/m, N = number of turns of coil = 7, i = current = 0.540 A and L = length of coil = πND where N = number of turns of coil = 7 and D = diameter of coil = 30.0 cm = 0.30 m.

So, B = μ₀Ni/L

= μ₀Ni/πND

= μ₀i/πD

Substituting the values of the variables into the equation, we have

B = μ₀i/πD

= 4π × 10⁻⁷ H/m × 0.540 A/(π × 0.30 m)

= 4 × 10⁻⁷ H/m × 0.540 A/0.30 m

= 2.16 × 10⁻⁷ HA/m/0.30 m

= 7.2 × 10⁻⁷ T

Since this magnetic field is at 45° to the horizontal, its horizontal comoonent equals the horizontal component B' of the earth's magnetic field.

So, Bcos45° = B'

B' = (7.2 × 10⁻⁷ T)cos45°

B' =  5.09 × 10⁻⁷ T

b. What is the total magnitude of the Earth's magnetic field at this location?

Since the angle of dip at this location is 11.0° and B" is the magnetic field at this location, the horizontal component of B" = B'

So B"sin11.0° = 5.09 × 10⁻⁷ T

B" = 5.09 × 10⁻⁷ T/sin11.0°

B" = 5.09 × 10⁻⁷ T/0.1908

B" = 26.68 × 10⁻⁷ T

B" = 2.668 × 10⁻⁶ T

B" ≅ 2.67 × 10⁻⁶ T

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hope this !

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles