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Tanzania [10]
3 years ago
6

A positive charge distribution exists within a nonconducting spherical region of radius a. The volume charge density ρ is not un

iform but varies with the distance r from the center of the spherical charge distribution, according to the relationship ρ=βr for 0<=0<=a, where β is a positive constant, and ρ=0, and r>a.A. Show that the total charge Q in the spherical region of radius a is βπa^4B. In terms of β,r,a and fundamential constants, determine the magnitude of the electric field at a point a from distance r from the center of the spherical charge distribution for each of the following cases.i. r>aii. r=aiii 0
Physics
1 answer:
baherus [9]3 years ago
5 0

A negative charge and a positive charge

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A coil of wire consists of 20 turns, each of which has an area of 0.0015 m2. A magnetic field is perpendicular to the surface wi
stepan [7]

Answer:

magnitude of the induced emf in the coil is 0.0153 V

Explanation:

Given data

no of turns = 20

area = 0.0015 m²

magnitude  B1 = 4.91 T/s

magnitude  B2 = 5.42 T/s

to find out

the magnitude of the induced emf in the coil

solution

we know here

emf = -n A d∅ /dt

so here n = 20 and

A = 0.0015

and d∅ = B2 - B1 = 5.42 - 4.91

d∅ = 0.51 T and dt  at 1 sec

so  put all value

emf = -n A d∅ /dt

emf = -20 (0.0015) 0.51 / 1

emf = - 0.0153

so magnitude of the induced emf in the coil is 0.0153 V

7 0
3 years ago
A spherical bowling ball with mass m = 3.6 kg and radius R = 0.101 m is thrown down the lane with an initial speed of v = 8.7 m/
luda_lava [24]

Answer:

1)  The magnitude of the angular acceleration = 67.92 rad/s^{2}

2) Magnitude of the linear acceleration = 2.744 m/s^{2}

3) How long does it take the bowling ball to begin rolling without slipping = 0.906 s

4) How long does it take the bowling ball to begin rolling without slipping = 6.75 m

5) the final velocity is 6.21 m/s

Explanation:

the given information :

Bowling mass m = 3.6 kg

Radius = 0.101 m

Initial speed v_{0} = 8.7 m/s

Coefficient of kinetic friction μ = 0.28

1) he magnitude of the angular acceleration of the bowling ball is

F = m a

F_{g}  = μ N  ,   N = m g

F_{g}  = μ m g

1) The magnitude of the angular acceleration of the bowling ball as it slides down the lane:

momen inersia of Bowling ball I = (2/5) m R^{2}

torque τ = I α

τ = F R

I α = F R

(2/5) m R^{2}  α = μ m g R

α = (5 μ g / 2R) μ g R

  = (5 x 0.28 x 9.8/ 2 x 0.101)

  = 67.92 rad/s^{2}

2) Magnitude of the linear acceleration of the bowling ball as it slides down the lane

F = - F_{g} , F_{k} is the force of kinetic friction

m a = - μ m g, remove m

the magnitude of linear accelaration is

a = μ g

  = (0.28) (9.8)

  = 2.744 m/s^{2}

3) The bowling ball takes time to begin rolling without slipping:

The linear speed, v_{t} = v_{0} - a t

                            v_{t}  =  v_{0} - μ g t

the angular speed, ω = ω0 + α t

                                ω = ω0 + (5  μ g/2R ) t

v_{t} = ω R

v_{0} - μ g t = ω0 R + (5  μ g/2R ) t R

7 μ g t/2 = v_{0} + ω0 R

hence,

t = (2 v_{0} + ω0 R)/  7 μ g

ω0 = 0 (no initial spin), therefore

t = 2 v_{0} / 7 μ g

 = 2 x 8.7 / 7 (0.28) (9.8)

 = 0.906 s

4) How long it takes for the bowling ball to begin rolling without slipping, S

S = v_{0}  t - (1/2) a t^{2}

  = (8.7) (0.906) - (1/2) (2.744) 0.906^{2}

  = 6.75 m

5) The final velocity

v_{t} = v_{0} - a t

v_{t} = 8.7 - (2.744) (0.906)

v_{t} = 6.21 m/s

4 0
3 years ago
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