What you miss in the second method is that the vertical component of the field is not equal to the total magnitude of the field. As you said, the horizontal components cancel out so you have to sum the vertical components only. You can tell that the second formula is wrong with no calculation. The field in the center of the ring should be zero (the field of each peice is all horizontal) and the formula does not produce this result.

What you miss in the second method is that the vertical component of the field is not equal to the total magnitude of the field. As you said, the horizontal components cancel out so you have to sum the vertical components only. You can tell that the second formula is wrong with no calculation. The field in the center of the ring should be zero (the field of each piece is all horizontal) and the formula does not produce this result.

What you miss in the second method is that the vertical component of the field isnot equal to the total magnitude of the field. As you said, the horizontal components cancel out so you have to sum the vertical components only. You can tell that the second formula is wrong with no calculation. The field in the center of the ring should be zero (the field of each peice is all horizontal) and the formula does not produce this result.

What you miss in the second method is that the vertical component of the field is not equal to the total magnitude of the field. As you said, the horizontal components cancel out so you have to sum the vertical components only. You can tell that the second formula is wrong with no calculation. The field in the center of the ring should be zero (the field of each peice is all horizontal) and the formula does not produce this result.