True or False The cross section of a solenoid is shown here. () The amount of cu

Question

True or False

The cross section of a solenoid is shown here. () The amount of current enclosed by the dashed loop is 10I. () The amount of current enclosed by the dashed loop is I. () The amount of current enclosed by the dashed loop is 6I. () The path integral of B dot ds for part 2 and part 4 are zero, because the B field is perpendicular to line 2 and line 4. () The path integral of B dot ds for part1 and part 3 are zero, because the B field is perpendicular to line 1 and line 3. () The path integral of B dot ds for part4 is B times length 1. () The path integral of B dot ds for part4 is zero, because B is nearly zero there. () The path integral of B dot ds for part4 is B times length 1. () The path integral of B dot ds for the entire dashed loop is B times length 1. () The path integral of B dot ds for the entire dashed loop is twice of B times length 1. () The B field strength due to an ideal solenoid is proportional to its current I. () The B field strength due to an ideal solenoid will increase if you increase the total number of turns and make it longer. () The B field strength due to an ideal solenoid will double if you make the solenoid twice long. () The B field strength due to an ideal solenoid will double if you pack the wires twice dense.

Explanation / Answer

The amount of current enclosed by the dashed loop = 6I as per the Ampere path.(All 6 wires having same current.)

The path integral of B dot ds for part 2 and parth 4 are NOT zero but the sum of B dot ds for line 2 and 4 comes out to be zero as they are of opposite sign.

The path integral of B dot ds for part 1 is B times the length of line 1.

The path integral of B dot ds for entire loop is B times the length of line 1. (since the B is zero outside)

The B field strength due to an ideal solenoid is mu * n * I.

So , it is proportional to I,

It is doubled when it is twice dense as n represents the density here.

PS: all other options are false.

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