Question

A device for accurately generating small forces between two wires can be created by the rectangular circuits shown in the figure on the worksheet for this problem. In the left circuit, the battery has an emf of ε₁ = 7 V and a resistor with fixed resistance R₁ = 6 ohms. In the right circuit, the battery has emf of ε₂ = 7 V and a variable resistor with resistance R₂ ohms. The circuits are L = 12 cm wide and D = 2 mm apart.

(a) To what resistance R₂ in ohms should the variable resistor be set to create a force of magnitude 2.0 x 10⁻⁵ N between the wires?

(b) Will the force be attractive or repulsive? Justify your answer by drawing the direction of the magnetic field in the vicinity of each wire on the circuit diagram and describing how the force is produced on each wire by those fields.

Answer 1

R, AAMAA A с within kiirry Iz ஆ மக Ez 1 B D KD » Q&=7V, Ry=612 = 2 mm = 2X103 m 6,=7 V, L =12 cm = 0.12in 2 current Howing in left circuit- 7/6 and in the light Sidle circuit- I = - 7 & Ri . Iz en R2 7 R2 froduced the wire by AB- magmatic field any point on B₂ = llo I2 2X10-3 22x107 x (4/R2, 2T D B₂ = 78104 -0 Ra Det er into this page". By Geight hand thumb Gule direction of By Now force on the segment AB - F = I x By XL F = () * (7X10 R2 x 0.12 2

2 0.02 But it is given that F = 2x10s N ( Also F2 = 2x105N from eq. : F,-F2) 2x105 7 x 7x104 x012 R2 oool R = 7x7 x 164x682 2X105 -) R = 4.912 of so we should set R₂ at 4.92 ♡ direction of B2 is "into the foge & director of Eurorent It is clownward' then by "left hand leule" direction of F, is towards height: ilarly direction of force F is towards left so we can that there is attraction between the wires. say Sími Can so