A solenoid of length 10 cm and 100 turns is wound over a magnetic core. The coercivity of the core material is 2000 A m ⁻¹ . The solenoid has a resistance of 2 and is connected in series with a battery of emf 20 V and internal resistance 1 , along with an unknown external resistor R . The value of R required so that the core is just demagnetized is ________ .

Step-by-step solution

To demagnetize the core, the magnetic intensity H produced by the solenoid must be equal to the coercivity of the core material. Given: Coercivity H_c = 2000 A m ⁻¹ Length of solenoid L = 10 cm = 0.1 m Number of turns N = 100 The magnetic intensity is given by H = ni = N L i . Substituting the given values: 2000 = 100 0.1 i 2000 = 1000 i i = 2 A. The total resistance of the series circuit is R_ total = R + R_ solenoid + r , where R_ solenoid = 2 and r = 1 . Using Ohm's law for the complete circuit: V = i R_ total 2