hi i have been reviewing physics but im little bit rusty therefore need some hel

Question

hi i have been reviewing physics but im little bit rusty therefore need some help , thank you !

here is the questions

1-)A uniform magnetic field of magnitude 1.00 T is directed perpendicular to the plane of a rectangular loop having dimensions 7.5 cm by 14 cm. Find the magnetic flux through the loop.

2-)A circular loop of wire of radius 12.5 cm is placed in a magnetic field directed perpendicular to the plane of the loop, as shown in the figure below. If the field decreases at the rate of 0.570 T/s in some time interval, what is the magnitude of the emf induced in the loop during this interval?

(a) If the current in the solenoid is 2.00 A, what is the magnetic flux through the square loop?


(b) If the current in the solenoid is reduced to zero in 4.00 s, what is the magnitude of the average induced emf in the square loop?

(a) What is the inductive time constant of the circuit?


(b) Calculate the current in the circuit 250 s after the switch is closed.


(c) What is the value of the final steady-state current?


(d) How long does it take the current to reach 81.0% of its maximum value?

hi i have been reviewing physics but im little bit rusty therefore need some help , thank you ! here is the questions 1-)A uniform magnetic field of magnitude 1.00 T is directed perpendicular to the plane of a rectangular loop having dimensions 7.5 cm by 14 cm. Find the magnetic flux through the loop. 2-)A circular loop of wire of radius 12.5 cm is placed in a magnetic field directed perpendicular to the plane of the loop, as shown in the figure below. If the field decreases at the rate of 0.570 T/s in some time interval, what is the magnitude of the emf induced in the loop during this interval? (a) What is the inductive time constant of the circuit? (b) Calculate the current in the circuit 250 ½s after the switch is closed. (c) What is the value of the final steady-state current? (d) How long does it take the current to reach 81.0% of its maximum value? = 6.00 V, L = 7.84 mH, and R = 3.96 ?. (a) If the current in the solenoid is 2.00 A, what is the magnetic flux through the square loop? (b) If the current in the solenoid is reduced to zero in 4.00 s, what is the magnitude of the average induced emf in the square loop? 4-)Consider the circuit shown in the figure below. Take = 1.00 cm on a side is placed inside a solenoid that has a circular cross section of radius r = 3.00 cm, as shown in the end view of the figure below. The solenoid is 21.0 cm long and wound with 102 turns of wire. 3-)A square, single-turn wire loop

Explanation / Answer

1) magnetic flux = A*B*cos(theta)

= 0.075*0.14*1*cos(0)

= 0.0105 T.m^2 or 10.5 mT.m^2

2)

induced emf = A*dB/dt

= pi*0.125^2*0.57

= 0.028 Volts or 28 mVolts

3) B = mue*N*I/L

= 4*pi*10^-7*102*2/0.21

= 1.22*10^-3 T

a) flux = A*B

= 0.01^2*1.22*10^-3

= 1.22*10^-7 T.m^2

b) induced emf = A*dB/dt

= 0.01^2*(1.22*10^-3 - 0)/4

= 3.05*10^-6 volts or 3.06 micro Volts

4)
a)T = L/R

= 7.84*10^-3/3.96

= 1.98 ms

b)

Imax = V/R = 6/3.96 = 1.515 A

at time t

I = Imax*(1 - e^(-t/T))

= 1.515*(1 - e^(-0.25*10^-3/1.98*10^-3))

= 0.18 A

c) I_final = Imax = 1.515 A

d)

I = Imax*(1 - e^(-t/T))

0.81*Imax = Imax*(1 - e^(-t/T))

e^(-t/T) = 1 - 0.81

t = -T*ln(0.19)

= 1.98*10^-3*ln(0.19)

= 3.29*10^-3 s

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