A cell is connected between two points of a uniformly thick circular conductor and i_1 and i_2 are the currents flowing in two parts of the circular conductor of radius aThe magnetic field at the centre of the loop will be

A cell is connected between two points of a uniformly thick circular c

1.	A cell is connected between two points of a uniformly thick circular conductor and i_1 and i_2 are the currents flowing in two parts of the circular conductor of radius aThe magnetic field at the centre of the loop will be
Answer» zero `(mu_0)/(4pi)(I_1-I_2)` `(mu_0)/(2a)(I_1+I_2)` `(mu_0)/a(I_1+I_2)` Solution :Let `l_1,l_2` be the lengths of the TWO parts PRQ and PSQ of the conductor and `rho` be the resistance per UNIT length of the conductor . The resistance of the portion PRQ will be `R_1 =l_1rho` The resistance of the portion PSQ will be `R_2 = l_2 rho` pot diff across P and ` Q = I_1 , R _1 = I_2 R_2` `I_1 l_1 rho = I_2 rho ` or `I_1 l_1 =I_2 l_2 ""....(1)` Magnetic field induction at the centre O DUE to currents through circular conductors PRQ and PSQ will be `=B_1 -B_2 =(mu_0)/2 (I_1l_1sin 90^@)/(r^2)-(mu_0)/(4pi)(I_2l_2sin 90^@)/r^2=0`

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A cell is connected between two points of a uniformly thick circular conductor and i_1 and i_2 are the currents flowing in two parts of the circular conductor of radius aThe magnetic field at the centre of the loop will be

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