Question
A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the coil. The radius of the coil changes as shown in figure. The graph of induced emf in the coil is represented by
![](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/521592/1/3853745/Picture7227.png)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/521592/1/3853746/Picture7228.png)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/521592/1/3853747/Picture7229.png)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/521592/1/3853748/Picture7230.png)
The correct answer is: ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/answer/521592/1/3853746/Picture7228.png)
![phi equals B A equals B cross times pi r to the power of 2 end exponent](data:image/png;base64,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)
(k = constant)
![therefore e equals fraction numerator d phi over denominator d t end fraction equals k.2 r fraction numerator d r over denominator d t end fraction](data:image/png;base64,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)
From 0 – 1, r is constant, \
hence, e = 0
From 1 – 2,
\
hence
Þ ![e proportional to t](data:image/png;base64,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)
From 2 – 3, again r is constant, \
hence e = 0
Related Questions to study
When a certain circuit consisting of a constant e.m.f. E an inductance L and a resistance R is closed, the current in, it increases with time according to curve 1. After one parameter (E, L or R) is changed, the increase in current follows curve 2 when the circuit is closed second time. Which parameter was changed and in what direction
![](data:image/png;base64,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)
When a certain circuit consisting of a constant e.m.f. E an inductance L and a resistance R is closed, the current in, it increases with time according to curve 1. After one parameter (E, L or R) is changed, the increase in current follows curve 2 when the circuit is closed second time. Which parameter was changed and in what direction
![](data:image/png;base64,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)
In the following figure, the magnet is moved towards the coil with a speed v and induced emf is e. If magnet and coil recede away from one another each moving with speed v, the induced emf in the coil will be
![](data:image/png;base64,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)
In the following figure, the magnet is moved towards the coil with a speed v and induced emf is e. If magnet and coil recede away from one another each moving with speed v, the induced emf in the coil will be
![](data:image/png;base64,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)
The equation
. where a, b, c are the sides of a ΔABC, and the equation
have a common root. The measure of
is-
in a right angled isosceles triangle, ratio of sides = 1:√2:1
base angles are = 45 degrees.
The equation
. where a, b, c are the sides of a ΔABC, and the equation
have a common root. The measure of
is-
in a right angled isosceles triangle, ratio of sides = 1:√2:1
base angles are = 45 degrees.
If in a ΔABC, (sin A + sin B + sin C)(sin A + sin B – sin C)= 3 sin A sin B, then –
the sine rule states that
a/sin A =b/sin B = c/sinC = 2R
this is used to find the relation of the angles and sides of the triangles.
If in a ΔABC, (sin A + sin B + sin C)(sin A + sin B – sin C)= 3 sin A sin B, then –
the sine rule states that
a/sin A =b/sin B = c/sinC = 2R
this is used to find the relation of the angles and sides of the triangles.
In the adjacent figure 'P' is any interior point of the equilateral triangle ABC of side length 2 unit –
![](data:image/png;base64,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)
If xa, xb and xc represent the distance of P from the sides BC, CA and AB respectively then xa + xb + xc is equal to -
area of equilateral triangle = √3a2/4
area of triangle = 1/2 x base x height
In the adjacent figure 'P' is any interior point of the equilateral triangle ABC of side length 2 unit –
![](data:image/png;base64,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)
If xa, xb and xc represent the distance of P from the sides BC, CA and AB respectively then xa + xb + xc is equal to -
area of equilateral triangle = √3a2/4
area of triangle = 1/2 x base x height
The expression
is equal to -
In a triangle ABC, cos A = (b2+c2-a2)/2bc
The expression
is equal to -
In a triangle ABC, cos A = (b2+c2-a2)/2bc
In the figure, if AB = AC,
and AE = AD, then x is equal to
![](data:image/png;base64,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)
exterior angle = sum of interior opposite angles is a property of triangles
sum of interior angles of a triangle = 180 degree
In the figure, if AB = AC,
and AE = AD, then x is equal to
![](data:image/png;base64,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)
exterior angle = sum of interior opposite angles is a property of triangles
sum of interior angles of a triangle = 180 degree
Statement- (1) : The tangents drawn to the parabola y2 = 4ax at the ends of any focal chord intersect on the directrix.
Statement- (2) : The point of intersection of the tangents at drawn at P(t1) and Q(t2) are the parabola y2 = 4ax is {at1t2, a(t1 + t2)}
Statement- (1) : The tangents drawn to the parabola y2 = 4ax at the ends of any focal chord intersect on the directrix.
Statement- (2) : The point of intersection of the tangents at drawn at P(t1) and Q(t2) are the parabola y2 = 4ax is {at1t2, a(t1 + t2)}
Statement- (1) : PQ is a focal chord of a parabola. Then the tangent at P to the parabola is parallel to the normal at Q.
Statement- (2) : If P(t1) and Q(t2) are the ends of a focal chord of the parabola y2 = 4ax, then t1t2 = –1.
slopes at the two extremeties of a focal chord are : (t,-1/t)
this property is used to explain the behaviour of tangents and normals at the respective points.
Statement- (1) : PQ is a focal chord of a parabola. Then the tangent at P to the parabola is parallel to the normal at Q.
Statement- (2) : If P(t1) and Q(t2) are the ends of a focal chord of the parabola y2 = 4ax, then t1t2 = –1.
slopes at the two extremeties of a focal chord are : (t,-1/t)
this property is used to explain the behaviour of tangents and normals at the respective points.