Q. 11

# Suppose the loop in Exercise 6.4 is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T s^{–1}. If the cut is joined and the loop has a resistance of 1.6Ω , how much power is dissipated by the loop as heat? What is the source of this power?

Answer :

Given: Length of rectangular wire = 8 cm

Breadth of rectangular wire = 2 cm

The area of the rectangular wire can be calculated as follows:

A = l × b

A = 8cm × 2cm = 16 cm^{2}= 16 × 10^{-4} m^{2}

Initial Magnitude of magnetic field B = 0.3T

Velocity of the loop, v =1 cms^{-1}

The rate of decrease of the magnetic field i.e.

The e.m.f developed in the rectangular loop is given as:

dФ is the change in the flux across the loop = AB

⇒

Or

Therefore, substituting the values in above equation, we get:

e = 16×10^{-4} m^{2}× 0.02 Ts^{-1}

⇒ e = 0.32 × 10^{-4}V

The current induced in the loop can be calculated as follows:

i = e/r

i = (0.32 × 10 ^{- 4})/1.6

⇒ i = 2 × 10 ^{- 5}A

The Power loss or dissipation can be calculated as follows:

P = i^{2}R

Where, R is resistance = 1.6Ω

⇒ P = (2 × 10^{-5}A)^{2} × 1.6Ω

⇒ P = 6.4×10^{-10} W

The source of the power is an external agent. This is due to change in the magnetic field with time.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSA jet plane is travelling towards west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the having a span of 25 m, if the Earth’s magnetic field at the location has a magnitude of 5 × 10–4 T and the dip angle is 30°.NEXTA square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of 8 cm s–1 in the positive x - direction in an environment containing a magnetic field in the positive z - direction. The field is neither uniform in space nor constant in time. It has a gradient of 10–3 T cm–1 along the negative x - direction (that is it increases by 10–3 T cm–1 as one moves in the negative x - direction), and it is decreasing in time at the rate of 10–3 T s–1. Determine the direction and magnitude of the induced current in the loop if its resistance is 4.50 mW.

RELATED QUESTIONS :

A. Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase : current or voltage?

B. Without making any other change, find the value of the additional capacitor to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.

Physics - Board Papers