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A coil 4.00 cm in radius, containing 500 turns, is placed in a uniform magnetic field that varies with time according to B = (0.0120 T/s)t + (3.00 x 10-5 T/s4)t4. The coil is connected to a 600 Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil. What is the current in the resistor at time t = 5.00 s?

User Mcont
by
7.7k points

2 Answers

3 votes

Answer:

The current in the resistor is 1.1304 mA.

Step-by-step explanation:

Given that,

Radius = 4.00 cm

Number of turns = 500

Magnetic field
B=(0.0120)t+(3.00*10^(-5))t^4

Resistance
R = 600\Omega

Time t = 5.00 s

We need to calculate the emf

Using formula of emf


\epsilon=NA(dB)/(dt)

Where, A = area

N = number of turns

B = magnetic field

Put the value into the formula


\epsilon = 500*\pi*(4.00*10^(-2))^2(d)/(dt)((0.0120)t+(3.00*10^(-5))t^4)


\epsilon=500*\pi*(4.00*10^(-2))^2*(0.0120+1.2*10^(-4))t^3

We need to calculate the current in the resistor at t = 5.00

Using formula of current


\epsilon=IR


I=(\epsilon)/(R)

Where, R = resistance

Put the value into the formula


I=(500*\pi*(4.00*10^(-2))^2*(0.0120+1.2*10^(-4))t^3)/(600)

Put the value of t in equation (II)


I=(500*\pi*(4.00*10^(-2))^2*(0.0120+1.2*10^(-4))(5.00)^3)/(600)


I=0.00011304\ A


I=1.1304*10^(-3)\ A


I=1.1304\ mA

Hence, The current in the resistor is 1.1304 mA.

User Raulriera
by
6.9k points
3 votes

Answer:

i = 1.13\times 10^{-4}A

Step-by-step explanation:

r = radius of the coil = 4 cm = 0.04 m

Area of coil is given as

A = πr²

A = (3.14) (0.04)² = 0.005024 m²

N = Number of turns = 500

R = Resistance = 600 Ω

B = magnetic field = (0.0120)t + (3 x 10⁻⁵) t⁴

Taking derivative both side relative to "t"


(dB)/(dt)= (0.0120 + (12* 10^(-5))t^(3))

Induced current is given as


i = \left ( (NA)/(R) \right )\left ( (dB)/(dt) \right )


i = \left ( (NA)/(R) \right ) (0.0120 + (12* 10^(-5))t^(3))

inserting the values at t = 5


i = \left ( ((500)(0.005024))/(600) \right ) (0.0120 + (12* 10^(-5))5^(3))


i = 1.13* 10^(-4)A

User Bolkay
by
6.9k points