Three point charges $$+$$ q each are fixed at $$A(L/2$$,$$L/2$$,$$0)$$,$$B($$−$$L/2$$,$$L/2$$,$$0)$$,$$C(0$$,−L,$$0)$$. A fourth point charge – q and mass ‘m’ is kept on $$z-axes$$ at D (0$$,$$0$$,$$Z) with Z<

Correct option is 4π3∈0mL33q2

Questions

Three point charges + q each are fixed at $A (L / \sqrt{2}, L / \sqrt{2}, 0), B (- L / \sqrt{2}, L / \sqrt{2}, 0), C (0, - L, 0)$ . A fourth point charge – q and mass ‘m’ is kept on z-axes at D (0,0,Z) with Z<<L and released, the minimum time taken by the fourth charge to cross the xy-plane is nearly (neglect effect of gravity)

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2π3∈0mL33qm2m

π3∈0mL3q2m

2π3∈0mL33q2

π3∈0mL33q2

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detailed solution

Correct option is D

Fnet=3Fcos⁡θ=−314πϵ0q2r2zr=−3q2z4π∈0r3≈−3q2z4π∈0L3 ∵r=L2+z2r≈L for z <

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Three point charges + q each are fixed at A(L/2,L/2,0),B(−L/2,L/2,0),C(0,−L,0). A fourth point charge – q and mass ‘m’ is kept on z-axes at D (0,0,Z) with Z<<L and released, the minimum time taken by the fourth charge to cross the xy-plane is nearly (neglect effect of gravity)

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