I’m having a relatively hard time in understanding Griffith’s explanation of why the radial component of a magnetic field of a solenoid should be zero. He says, "If B(r) were positive, if we reversed the direction of the current, B(r) would be negative. But switching I is physically equivalent to turning the current upside down, and that certainly should not alter the radial field".
I understand the first half of the explanation but I’m just not able to get why the radial field should not be altered if I turn the current upside down. I’ll be thankful if anyone explains why.