utorial Exercise A uniformly charged ring of radius 10.0 cm has a total charge o
ID: 1883976 • Letter: U
Question
utorial Exercise A uniformly charged ring of radius 10.0 cm has a total charge of 47.5 C. Find the electric field on the axis of the ring at the following distances from the center of the ring. (Choose the x-axis to point along the axis of the ring.) (a) 1.00 cm (b) 5.00 cm (c) 30.0 cm (d) 100 cm Step 1 The electric field is zero at the center of the ring and at an infinite distance from the ring. If the maximum field is in the range from 1.00 cm to 100 cm, we should be able to tell this from our analysis below. The field polnts away from the ring along its axis because the ring has a unlform positive charge. The charge In the ring contributes to total field components that sum to zero parallel to the face of the ring. The components perpendicular to the face of the ring add together to form the total electric field along the axis of the ring Step 2 We evaluate the field due to a continuous charge distribution rather than a group of individual charges Step 3 The total electric field at point P, a distance from the center of a ring of radius a, Is given by the following equation. Substituting the given values for the charge and radius, we have the following kexQ (x2a2)3/2 (8.99 × 109 N·m2/C2) x 10-6 Cx P. x 105 N m2/C Submit Skip (you cannot come back)Explanation / Answer
As per given formula, E= Ke X Q / (x2 + a2)3/2
Case a) distance from center= 1 cm
=> E= 8.99X109 X 47.5 X 10-6 / ((10-2)2 + (10-2)2)3/2
=> E = 1.51 X 1011 N/C
Case b) distance from center= 5 cm
=> E= 8.99X109 X 47.5 X 10-6 / ((5X10-2)2 + (10-2)2)3/2
=> E = 3.22 X 109 N/C
Case c) distance from center= 30 cm
=> E= 8.99X109 X 47.5 X 10-6 / ((30X10-2)2 + (10-2)2)3/2
=> E= 1.58 X 107 N/C
Case d) distance from center= 100 cm
=> E= 8.99X109 X 47.5 X 10-6 / ((100X10-2)2 + (10-2)2)3/2
=> E= 4.27 X 105 N/C
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