The fields F and G are shown below. Each field has no k -component and is indepe

Question

The fields F and G are shown below. Each field has no k -component and is independent of z. All the axes have the same scale. Field F Field G (a) What are the signs of divF and divG at the origin? divF(0, 0, 0)-| negative divG(0, 0,0 negativeiX (b) Are F and G curl free fields? | 3 ra-Select 4 : Select ? (c) Is there a closed surface around the origin such that F has a nonzero flux through it?" -Select-- (d) Is there a closed curve around the origin such that G has a nonzero circulation around it? Selec

Explanation / Answer

(a) div F(0,0,0) will be negative. The field lines are converging at (0,0,0).

     div G(0,0,0) will be zero. The field lines are neither converging nor diverging. The field lines are parallel.

(b) True, both F and G are curl-free fields. F and G are non-circulating fields. Hence, curl will be zero.

(c) True. As the electric field flux is converging at (0,0,0). So, the closed surface with (0,0,0) inside it will have nonzero flux through it.

(d) False. As the electric field flux is parallel throughout the space, there will not be any closed curve in which G will have nonzero circulation around it.

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