KNOW THE ANSWER BUT I WOULD LIKE TO KNOW HOW TO GET THERE, THANK YOU 14. A squar

Question

KNOW THE ANSWER BUT I WOULD LIKE TO KNOW HOW TO GET THERE, THANK YOU

14. A square wire loop with 1.0m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field as shown in the picture below. The loop contains an ideal battery with emf 1.5 V. If the magnitude of the field varies with time according to B = 7.2 + 1.6t, with B in Teslas and t in seconds, what are (i) the net emf in the circuit, and (ii) the direction of the (net) current around the loop? A) 2.3V, counterclockwise. B) 2.3 V, clockwise. C) 0.7V, counterclockwise. D) 0.7V, clockwise. E) 3.1 V, counterclockwise. V bat

Explanation / Answer

l = length of side of square = 1m

here half of the loop is in magnetic field

effective area of loop A = l^2/2 = 1/2 = 0.5 m^2

magnetic flux = B*A

induced emf = rate of change in flux

emf = (d/dt)*(B*A)

emf = A*dB/dt

emf = 0.5*1.6

emf = 0.8 V

at t = 0

magnetic field B = 7.2 T

at t = 1

magnetic field B = 7.2 + 1.6 = 8.8 T

here the magnetic field is increasing

the induced magnetic field is INTO the page

the induced cuurent is clockwise

the induced emf is clockwise ( negative)

net emf = e - ein = 1.5 - 0.8 = 0.7 V

the current due to battery is counter clockwise

induced current is clockwise

e > ein

the net current flows counter clockwise

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