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Artist 52 [7]
3 years ago
11

The magnitude J(r) of the current density in a certain cylindrical wire is given as a function of radial distance from the cente

r of the wire’s cross section as J(r) ! Br, where r is in meters, J is in amperes per square meter, and B ! 2.00 $ 105 A/m3.This function applies out to the wire’s radius of 2.00 mm. How much current is contained within the width of a thin ring concentric with the wire if the ring has a radial width of 10.0 mm and is at a radial distance of 1.20 mm?
Physics
1 answer:
Gennadij [26K]3 years ago
3 0

Answer:

18.1 × 10⁻⁶ A = 18.1 μA

Explanation:

The current I in the wire is I = ∫∫J(r)rdrdθ

Since J(r) = Br, in the cylindrical wire. With width of 10.0 μm, dr = 10.0 μm. r = 1.20 mm. We have a differential current dI. We integrate first by integrating dθ from θ = 0 to θ = 2π.

So, dI = J(r)rdrdθ

dI/dr = ∫J(r)rdθ = ∫Br²dθ = Br²∫dθ = 2πBr²

Now I = (dI/dr)dr at r = 1.20 mm = 1.20 × 10⁻³ m and dr = 10.0 μm = 0.010 mm = 0.010 × 10⁻³ m

I = (2πBr²)dr = 2π × 2.00 × 10⁵ A/m³ × (1.20 × 10⁻³ m)² × 0.010 × 10⁻³ m  =  0.181 × 10⁻⁴ A = 18.1 × 10⁻⁶ A = 18.1 μA

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A rectangular coil of dimensions 5.40cm x 8.50cm consists of25 turns of wire. The coil carries a current of 15.0 mA.
Kazeer [188]

Answer:

(a) Magnetic moment will be 17.212\times 10^{-4}A-m^2

(b) Torque will be 6.024\times 10^{-4}N-m

Explanation:

We have given dimension of the rectangular 5.4 cm × 8.5 cm

So area of the rectangular coil A=5.4\times 8.5=45.9cm^2=45.9\times 10^{-4}m^2

Current is given as i=15mA=15\times 10^{-3}A

Number of turns N = 25

(A) We know that magnetic moment is given by magnetic\ moment=NiA=25\times 45.9\times 10^{-4}\times 15\times 10^{-3}=17.212\times 10^{-4}A-m^2

(b) Magnetic field is given as B = 0.350 T

We know that torque is given by \tau =BINA=0.350\times 15\times 10^{-3}\times 25\times 45.9\times 10^{-4}=6.024\times 10^{-4}N-m

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2 years ago
Why doesn't the force of gravity change the speed of a bowling ball as it rolls along a bowling lane?
Oliga [24]
Because the gravitational force, which points downward, is perfectly balanced by the normal reaction of the floor of the bowling lane, which points upward. The two forces are equal in magnitude, so the net force acting vertically on the bowling ball is zero, therefore there is no acceleration along this direction. Moreover, since the ball is moving in the horizontal direction, the gravitational force has no component along this direction, so it does not change the velocity of the ball.
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How much pressure is created when you apply a
Alekssandra [29.7K]
Pressure
= Force/Area

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g a stone with mass m=1.60 kg IS thrown vertically upward into the air with an initial kinetic energy of 470 J. the drag force a
otez555 [7]

Answer:

Height reached will be 28.35 m

Explanation:

Here we can use the work energy theorem to find the maximum height

As we know by work energy theorem

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-mgh - F_f h = 0 - \frac{1}{2}mv_i^2

now we will have

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h = 28.35 m

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